Question

sinA(1+tanA) + cosA (1+cotA) = secA + cosecA​

Answer 1

Step-by-step explanation:

Given SinA(1+tanA) + cosA (1+cotA) = secA + cosecA

• Given sin A (1 + tan A) + cos A(1 + cot A)
•      = sin A (1 + sin A / cos A) + cos A (1 + cos A / sin A)
•     = sin A / cos A (sin A  + cos A) + cos A / sin A (sin A + cos A)
•    = (sin A + cos A) (sin A / cos A + cos A / sin A)
•        =  (sin A + cos A)(sin^2 A + cos ^2 A / cos A sin A)
•        = sin A + cos A ( 1 / cos A sin A)
•     =   sin A/ cos A sin A  + cos A / cos A sin A
•      = sec A + cosec A  (proved)

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https://brainly.in/question/147206