Question

prove that
$\sqrt{sec ^{2} + cosec {}^{2} } = tan \: + cot$
​

Answer 1

Answer:

Proved.

Step-by-step explanation:

Convert LHS in sin and cos.

If this whole process is difficult for you you can change both sides in sin cosine and equate an intermediate resultt.

Answer 2

Prove that :-

• $\sf \sqrt{sec^2 \: + cosec^2} = tan+cot$

To Prove :

• L.H.S = R.H.S

• i.e. $\sf \sqrt{sec^2 \theta \: + cosec^2 \theta} = tan \theta \: + cos \theta$

Solution :

L.H.S = $\sf \sqrt{sec^2 \theta \: + cosec^2 \theta}$

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$\sf \longrightarrow \: \sqrt{(1 + tan^2 \theta) + (1 + cot^2 \theta}$

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$\sf \longrightarrow \: \sqrt{2 + tan^2 \theta + cot^2 \theta}$

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$\sf \longrightarrow \: \sqrt{tan^2 \theta + cot^2 \theta + 2 \: tan \theta \: cot \theta}$

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$\sf \longrightarrow \: (tan\theta + cot \theta)^2$

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$\sf \longrightarrow \: (tan\theta + cot \theta) = R.H.S$

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L.H.S = R.H.S

Hence, Proved!