Question

Prove that sinA(1+tanA) + cosA(1+cotA) = secA + cosecA

Answer 1

Answer:

here's ur prove

Step-by-step explanation:

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sin(1+sin/cos)+cos(1+cos/sin)

sin(cos+sin/cos)+cos(sin+cos/sin)

(sin+cos)(sin/cos+cos/sin)

(sin+cos)/(sincos)

1/cos+1/sin

sec+cosec

Answer 2

Answer:

sinA * (1 + tan) + cosA * (1 + cotA) = secA + cscA

LS = sinA * (1 + sinA/cosA) + cosA * (1 + cosA/sinA)

= sinA + sin^2A/cosA + cosA + cos^2A/sinA => rewrite as:

= sinA + cos^2A/sinA + cosA + sin^2A/cosA

= (sin^2A + cos^2A)/sinA + (cos^2A + sin^2A)/cosA

= 1/sinA + 1/cosA

= cscA + secA

= secA + cscA = RS