Q7 Prove (sin A + cosec A)2 + ( cos A + sec A = 7+tan A + cot?A
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Step-by-step explanation:
(sin A + cosec A)² + (cos A + sec A)²
=sin²A + cosec²A + 2 sin A cosec A + cos²A + sec²A + 2 cos A sec A
=(sin²A + cos²A) + 2 sin A x 1/sin A + 2 cos A x 1/cos A + cosec²A + sec²A
=1 + 2 + 2 + (1 + cot²A) + (1 + tan²A)
=5 + 1 + 1 + cot²A + tan²A
=7 + cot²A + tan²A
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