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Step 1 :

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Sum and difference formulas :

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$\"\"$

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Step 2 : The values are $\"\"$ and $\"\"$ .

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Since $\"\"$ then $\"\"$ and $\"\"$

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The angle $\"\"$ is lies in first quadrant.

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$\"\"$

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The point $\"\"$ is lies on the curve of radius $\"\"$

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Thus,

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$\"\"$

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Since the point $\"\"$ is lies in first quadrant consider $\"\"$

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The value of cosine function is $\"\"$

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Step 3 :

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Since $\"\"$ then $\"\"$ and $\"\"$

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The angle $\"\"$ is lies in fourth quadrant. $\"\"$

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The point $\"\"$ is lies on the curve of radius $\"\"$ Thus,

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$\"\"$

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Since the point $\"\"$ is lies in first quadrant consider $\"\"$ The value of cosine function is $\"\"$

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Step 3 :

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(a)

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The expression is $\"\"$

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From the sum and difference formulas for the sine function.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in above equation. $\"\"$

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Thus,

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$\"\"$

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Step 3 :

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(b)

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The expression is $\"\"$

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From the sum and difference formulas for the sine function.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Thus,

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$\"\"$

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Step 3 :

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(c)

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The expression is $\"\"$

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From the sum and difference formulas for the sine function.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Thus,

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$\"\"$

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Step 3 :

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(d)

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The expression is $\"\"$

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Rewrite the expression :

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$\"\"$ Evaluation of $\"\"$ :

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From the sum and difference formulas for the sine function.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Thus,

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$

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$\"\"$

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Thus,

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$\"\"$ Solution :

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(a) $\"\"$

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(b) $\"\"$

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(c) $\"\"$

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(d) $\"\"$