Question

cosec²67°-tan²23° = 1 prove

Answer 1

Hi mate

here is ur answer

cosec^2 67° - tan^2 23°. = 1

sec^2 67° - tan ^2 23° = 1 [ complementary angles]

1=1 [ identity]

I hope this will help you

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Answer 2

Hey dear
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Here your answer

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$lhs = { \csc(67) }^{2} - { \tan(23) }^{2} \\ \\ \: \: \: \: \: \: \: \: = { \csc(90 - 23) }^{2} - { \tan(23) }^{2} \\ \\ \: \: \: \: \: \: \: \: = {sec}^{2} (23) - ( {sec}^{2}(23) - 1) \\ \\ \: \: \: \: \: \: \: \: = {sec(23)}^{2} - {sec}^{2}(23) + 1 \\ \\ \\ \: \: \: \: \: \: \: = 1 \\ \\ \: \: \: \: \: \: \: = rhs \\ \\ hope \: it \: helps \: you$