Question

`If sec^(-1 (tan theta +cosec^(-1 (tan theta =(pi /(2 then the exhaustive range of'theta' is`​

Answer 1

Answer:

-1

Step-by-step explanation:

  sec θ = √2 ⇒ cos θ = 12√12 ∴ sin θ = ±1−cos2θ−−−−−−−−√1−cos2θ = ±1−12−−−−−√1−12 = ±12√12 Since θ lies in the fourth quadrant, so sin θ is –ve and cos q is +ve. ∴ sin θ = −12√−12, cosec θ = √2 tan θ = sinθcosθsinθcosθ = −12√−12 x 2√121 = –1 ⇒ cot θ = –1 ∴ 1+tanθ+cosecθ1+cotθ−cosecθ1+tanθ+cosecθ1+cotθ−cosecθ = 1−1−2√1−1+2√=−1