Question

Prove 2 sin square theta+4 sec squaretheta +5 cot squaretheta + 2 cos square theta- 4 tan square theta -5 cosecSquare theta =1

Answer 1

Solution :

Here, I am using A instead of theta.

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We know the Trigonometric identities:

i ) sin²A + cos²A = 1

ii ) sec²A - tan² A = 1

iii ) cot²A-cosec²A = -1

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LHS = 2sin²A+4sec²A+5cot²A

+ 2cos²A-4tan²A-5cosec²A

= 2(sin²A+cos²A)+4(sec²A-tan²A)

+5( cot²A - cosec²A )

= 2 × 1 + 4 × 1 + 5 × ( -1 )

= 2 + 4 - 5

= 6 - 5

= 1

= RHS

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