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

1.	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» 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 + sec²α + 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

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»

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 + sec²α + 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