Question

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

Answer 1

Step-by-step explanation:

Prove that

SinA(1+tanA)+CosA(1+CotA) = secA + cosecA

Solutions

LHS

Sin(1 + tanA) + cosA(1+cotA)

SinA + Sin^2A/cosA + cosA + Cos^2A/sinA

On arranging

SinA + cos^2A/sinA + CosA + Sin^2A/cosA

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

1/sinA + 1/cosA

cosecA + SecA

Hence

LHS = RHS

Trigonometry identity used

Sin^2A + cos^2A = 1

1/sinA = cosecA

1/cosA = SecA

Addition , Multiplication is too used while

proving the expression .