Question

Verify.
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Answer 1

Explanation:

1+sinx/cosx = cosx/1/sinx

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cosx•cosx = (1+sinx)(1-sinx)

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cos^2x = 1- sinx +sinx -sin^2x

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cos^2x = 1 -sin^2x

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cos^2x + sin^2x = 1

Answer 2

Explanation:

1+sinx / cosx = cos x / 1-sinx

Cross multiply across the equation,

(1+sinx)(1-sinx) = cosx × cosx= cos^2x

Opening the bracket, we have

1 -sinx + sinx - sin^2x =cos^2x

1- sin^2x =cos^2x ---------------1

Recall that sin^2x + cos^2x =1

Therefore, from eqn 1,

1 = cos^2x + sin^2x

So

1+sinx / cosx = cos x / 1-sinx is correct

Note:

cos^2x means cos square x

sin^2x means sin square x