Question

(cosectheta-sin theta)(sec theta-cos theta)(tan theta+cot theta)=1​

Answer 1

Step-by-step explanation:

(cosectheta-sin theta)(sec theta-cos theta)(tan theta+cot theta)

(1/sin A - sin A) ( 1/cosA - cosA)(tanA + 1/tanA)

(1-sin^2A/sinA)( 1-cos^2 A/ cosA) (tan^2A +1/cotA)

cos^2A /sinA sin^2A /cosA tan^2 A/ tanA

1/sinA cosA 1+ tan^2 A/tanA

sin^2A/sinA cos A 1+ tan^2A/tanA

tanA 1+tan^2 A /tanA

1+2 + tan^2 A/tanA

cot A + 2+ tan A = -1

squaring on both sides