Question

prove that tan theta minus cot theta by sin theta cos theta is equal to tan square theta minus cos square theta

Answer 1

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Answer 2

Answer:

Hence prove given below.

Step-by-step explanation:

Given : Expression $\frac{tan\theta-cot\theta}{(sin\theta)(cos\theta)}$

To prove : The expression is equal to $tan^2\theta-cot^2\theta$

Solution : The expression

$\frac{tan\theta-cot\theta}{(sin\theta)(cos\theta)}$

$=\frac{\frac{sin\theta}{cos\theta}-\frac{cos\theta}{sin\theta}}{(sin\theta)(cos\theta)}$

$=\frac{\frac{sin^2\theta-cos^2\theta}{cos\theta sin\theta}}{(sin\theta)(cos\theta)}$

$=\frac{sin^2\theta-cos^2\theta}{sin^2\theta)(cos^2\theta)}$

$=\frac{1}{cos^2\theta}-\frac{1}{sin^2\theta}$

$=sec^2\theta-cosec^2\theta}$

$=1+tan^2\theta-(1+cot^2\theta)$

$=1+tan^2\theta-1-cot^2\theta$

$=tan^2\theta-cot^2\theta$

The requited result.