Question

If (sin α + cosec α)² + (cos α + sec α)² = k + tan² α + cot² α, then the value of k is equal to

(1) 9

(2) 7

(3) 5

(4) 3

Answer 1

Answer is (2) 7

(sin α + cosec α)² + (cos α + sec α)² = k + tan² α + cot² α

sin² α + cosec² α + 2 sin α cosec α + cos² α + sec² α + 2 cos α sec α = k + tan² α + cot² α

sin² α + cos² α + cosec² α + sec² α + 2 sin α x + \(\frac{1}{sin\alpha}\) 2 cos α x \(\frac{1}{cos\alpha}\) = k + tan² α + cot² α

1 + 1 + cot² α + 1 + tan² α + 2 + 2 = k + tan² α + cot² α

7 + cot² α + tan² α = k + tan² α + cot² α

∴ k = 7