Question

Cosec square 67 degree minus 10 square 23 degree is equal to what

Answer 1

Answer:

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Answer 2

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Correct question ❓

$cosec ^{2} 67 \: - tan ^{2} 23 \: is \:equal \: to \: what$

Solution ✏

To find : cosec^2 (67)° - tan^2 (23) ° __eqn(1)

As we know that,

$tan(90 - \theta ) = \cot \theta$

also,

${ \tan}^{2} (90 - \theta ) = {cot}^{2} \theta$

So,

$replacing \: \\ tan ^{2} (23) \: by \: cot ^{2} (90 - 23)$

we will get,

cosec^2 (67) ° - cot^2 (90-23) °

cosec^2 (67) ° - cot^2 (67) °

$by \: identity \: we \: know \: that \\ 1 + \ {cot}^{2} \theta = {cosec}^{2} \theta \\ \\ that \: \: is \: \\ {cosec}^{2} \theta - {cot}^{2} \theta = 1$

so,

cosec^2 (67) ° - cot^2 (67) ° = 1

SO THE VALUE OF

COSEC^2 (67) ° - tan^2 (23) ° = 1

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