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Solve Trig?

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Write the trigonometric expression in terms of sine and cosine, and then simplify.
sin^2 θ (1 + cot^2 θ)
asked May 11, 2014 in TRIGONOMETRY by anonymous

1 Answer

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sin^2 θ (1 + cot^2 θ)

= sin^2 θ (1 + (cos^2 θ / sin^2 θ))                     [Since cotθ = cosθ / sinθ]

= sin^2 θ ((sin^2 θ + cos^2 θ) / sin^2 θ)

= sin^2 θ / sin^2 θ (sin^2 θ + cos^2 θ)

= 1 (sin^2 θ + cos^2 θ)

= sin^2 θ + cos^2 θ

The trigonometric expression in terms of sine and cosine is sin^2 θ + cos^2 θ.

 

answered May 12, 2014 by joly Scholar

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