Question 80

If (1 + sinA)/cosA + cosA/(1 + sinA) = x, then the value of x is

Solution

Expression : $$\frac{(1+sinA)}{cosA}+\frac{cosA}{(1+sinA)}$$

= $$\frac{(1+sinA)^2+(cosA)^2}{cosA(1+sinA)}$$

= $$\frac{(1+2sinA+sin^2A)+cos^2A}{cosA(1+sinA)}$$

= $$\frac{1+2sinA+1}{cosA(1+sinA)}$$ $$[\because sin^2A+cos^2A=1]$$

= $$\frac{2+2sinA}{cosA(1+sinA)} = \frac{2(1+sinA)}{cosA(1+sinA)}$$

= $$\frac{2}{cosA} = 2secA$$

=> Ans - (D)

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