Question

Q prove that tan cube theta upon 1 + 10 square theta + cot square theta upon 1 + cos squared theta equals to sec theta cosec theta minus 2 sin theta cos theta ??

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Answer 1

tan theta + 1 upon 10 is equal to 2 to prove that tan squared theta + 1 upon 10 square theta is equal to 2

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Answer 2

$Given \: tan \theta + \frac{1}{tan \theta} = 2 \: ---(1)$

/* On squaring both sides of the Equation (1), we get */

$\big( tan\theta + \frac{1}{ tan \theta}\big)^{2} = 2^{2}$

$\implies tan^{2} \theta + \frac{1}{tan^{2} \theta } + 2 \times tan\theta \times \frac{1}{tan \theta } = 4$

/* We know the , algebraic identity :

$\boxed { \pink { (a+b)^{2} = a^{2} + b^{2} + 2ab }}$

$\implies tan^{2} \theta + \frac{1}{tan^{2} \theta } + 2 = 4$

$\implies tan^{2} \theta + \frac{1}{tan^{2} \theta } \\= 4 - 2\\= 2$

Therefore.,

$\red { tan^{2} \theta + \frac{1}{tan^{2} \theta }} \green { = 2}$

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