prove that (1 + cot a minus cosec a)(1 + tan A + sec a )=2
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Answered by
3
Hey there!
L.H.S:
( 1 + cot A - cosec A) (1 + tan A + sec A)
= ( 1 + cosA/sinA - 1/sinA) ( 1 + sinA/cosA + 1/cosA)
= [(sin A + cos A - 1) / sin A] . [(cosA + sinA + 1) / cosA]
= [ (sin A + cosA)² - 1)] / sinA.cosA
= (sin²A + cos²A + 2sinA.cosA - 1) / SinA.cosA
= ( 1 + 2 sinA.cosA - 1) / sinA.cosA {∵ sin²A + cos²A = 1}
= 2 * sinA.cosA / sinA.cosA
= 2
= R.H.S
Answered by
1
Step-by-step explanation:
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