Question

please solve this question. which is -:

${cosec}^{2}67 - {tan}^{2}23$

Answer 1

cosec²67° - tan²23°

we know one thing ,
tanΘ = cot(90 - θ)
tan23° = cot(90° - 23°) = cot67°

hence,
cosec²67° - cot²67°

we know,
cosec²θ - cot²θ = 1

so, cosec²67° - cot²67° = 1

Answer 2

Heya user,
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We shall use the formula:

cosec²Ф - cot²Ф = 1;   and tan(90° - Ф) = cotФ

Now, here,
tan²23° = tan² ( 90° - 67° ) = cot² 67°

Now, cosec²67° - tan²23° = cosec²67° - cot²67° = 1; ☺