Question

prove the following trigonometric identitie

Answer 1

Heya
Here is your answer
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(sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A

opening the identity (a + b)² = a² + b² + 2ab

sin²A + cosec²A + 2*sinA*cosecA + cos²A + sec²A + 2*cosA*secA = R.H.S

We know that:
sin²A + cos²A = 1
cosec²A = 1 + cot²A
sec²A = 1 + tan²A
sinA * cosecA = 1
cosA * secA = 1

Putting and doing all the mentioned things above

1 + 1 + 1 + 2 + 2 + cot²A + tan²A = RHS

7 + cot²A + tan²A = 7 + cot²A + tan²A

Hence Proved
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Hope this helps! ^_^