Prove that Sin θ Sin( 90° - θ) - Cos θ Cos( 90° - θ) = 0

Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0

Sum

LHS = sin θ sin( 90° - θ) - cos θ cos( 90° - θ)

= sin θ . cos θ - cos θ . sin θ

= 0
= RHS
Hence proved.

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Prove the following trigonometric identities:

`sin theta/(1 - cos theta) = cosec theta + cot theta`

Prove the following trigonometric identity:

`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`

Prove the following identities:

`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`

Prove the following identities:

`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`

`(sec^2 theta-1) cot ^2 theta=1`

Prove that:

Sin⁴θ - cos⁴θ = 1 - 2cos²θ

Prove the following identity :

secA(1 - sinA)(secA + tanA) = 1

If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1

Prove that sec²θ – cos²θ = tan²θ + sin²θ.

Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A