Prove the trigonometric identity: tan^2 θ cos^2 θ = 1- cos^2 θ?

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Answer 1 · 2018-04-05T10:21:33

See below.

Identity:

$color(red)bb(tanx=sinx/cosx)$

RHS:

Substitute identity:

$sin^2(theta)/cos^2(theta)cos^2theta$

Cancelling:

$sin^2(theta)/cancel(cos^2(theta))cancel(cos^2theta)$

$sin^2(theta)$

Identity:

$color(red)bb(sin^2x+cos^2x=1)$

$:.$

$sin^2(theta)=1-cos^2(theta)$

$RHS-=LHS$