# trigonometry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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Verify tan x +2 cot x =sec x csc x+cot x

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LHS tan(x) + 2cot(x)

tan(x) + cot(x) + cot(x)

Quotient Identities: tan(θ) = sin(θ)/cos(θ) and cot(θ) = cos(θ)/sin(θ)

[sin(x)/cos(x) + cos(x)/sin(x)] + cot(x)

Rewrite the expression with common denominator.

[sin2(x) + cos2(x)]/[sin(x)cos(x)] + cot(x)

Pythagorean Identities: sin2(θ) + cos2(θ) = 1

1/[sin(x)cos(x)] + cot(x)

[1/sin(x)]*[1/cos(x)] + cot(x)

Reciprocal identities: 1/isn(θ)=coses(θ) and 1/cos(θ)=sec(θ).

coses(x)sec(x) + cot(x) RHS

Therefore tan(x) + 2cot(x) = sec(x)coses(x) + cot(x).

The trigonometric equation is tan x + 2 cot x = sec x csc x + cot x.

Right hand side identity = sec x csc x + cot x.

Using reciprocal identities : sec x = 1/cos x and csc x = 1/sin x.

sec x csc x + cot x = (1/cos x)(1/sin x) + cot x

= (1/cos x sin x) + cot x

Pythagorean Identities: sin2(x) + cos2(x) = 1.

= (sin2x + cos2x)/(cos x sin x) + cot x

= (sin2x/cos x sin x) + (cos2x/cos x sin x) + cot x

= (sin x/cos x) + (cos x/sin x) + cot x

Trigonometry identities : tan x = sin x/cos x and cot x = cos x/sin x.

= tan x + cot x + cot x

= tan x + 2 cot x

= Left hand side identity.