Question

2sin²θ + 4sec²θ + 5cot²θ + 2cos²θ – 4tan²θ – 5cosec²θ =1,Prove it by using trigonometric identities.

Answer 1

We can solve the question by using trigonometric identities

such as

$sin^{2} \alpha+cos^{2}\alpha =1$

$1+tan^{2}\alpha = sec^{2}\alpha$

$1+cot^{2} \alpha = cosec^{2}\alpha$

Apply this equation in above question.

Answer 2

Here I am using A instead of

theta .

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We know the Trigonometric

Identities :

1 ) sin²A + cos²A = 1

2 ) sec²A - tan² A = 1

3 ) cosec²A - cot ² A = 1

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Now ,

LHS = 2sin²A + 4sec²A + 5cot²A

+ 2cos²A - 4tan²A - 5cosec²A

Rearranging the terms ,we get

= 2sin²A + 2cos²A + 4sec²A

- 4tan²A - 5cosec²A + 5cot²A

= 2(sin²A + cos² A )

+ 4( sec²A - tan²A )

- 5( cosec² A - cot²A )

= 2 + 4 - 5

= 6 - 5

= 1

= RHS

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