Question

prove that 2sinsquarethitha+4secsquarethitha+5cotsquarethitha+2cossquarethitha-4tansquarethitha-5cosecsquarethitha=1​

Answer 1

Here I am using A instead of theta.

LHS = 2sin²A+4sec²A+5cot²A

+2cos²A-4tan²A-5cosec²A

Rearranging the terms, we get

= 2sin²A+2cos²A+4sec²A-4tan²A

+5cot²A-5cosec²A

=2(sin²A+cos²A)+4(sec²A-tan²A)

-5(cosec²A-cot²A)

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We know the Trigonometric identities:

i) sin²A+cos²A = 1

ii ) sec²A - tan²A = 1

iii) cosec²A-cot²A = 1

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= 2+4-5

= 6-5

= 1

= RHS

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