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Trig Identity (Discussion)

The_Ahmad said – Sat, 11 Apr 2009 13:46:48 -0000 ( Link )

Can anyone solve this trig identity. State restrictions on theta (x) if they apply.

tan x / cos x = sin x / 1 – sin2 (squared) x

It seemed simple enough but I seem to be having some trouble.

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  1. oLahav said – Tue, 14 Apr 2009 16:50:49 -0000 ( Link )

    tan x = sin x / cos x (that’s one of your basic identities). So you plug that in, and now the left side equals sin x / cos x / cos x which reduces to sin x / cos2 x. Then by the basic identity sin2 x + cos2 x = 1, you can rearrange and get sin x / (1 – sin2 x).

    I hope this helps.

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  2. Sureshbala said – Thu, 23 Apr 2009 06:50:51 -0000 ( Link )

    Given

    \frac{Tan \theta}{Cos \theta} = \frac{Sin \theta}{1-Sin^2\theta}
    \frac{\frac{Sin \theta}{Cos \theta}}{Cos \theta} = \frac{Sin \theta}{1-Sin^2\theta}
    \frac{Sin \theta}{Cos^2 \theta}=\frac{Sin \theta}{Cos^2\theta}

    So this holds for every value of \theta other than those value of \thetafor which Cos \theta = 0

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