Question

Prove this pizz..

(1+cotA-cosecA)(1+tanA+secA) = 2

Answer 1

Trigonometry,

We have to prove that,
(1+cotA-cosecA)(1+tanA+secA) = 2

Now
LHS = (1+cotA-cosecA)(1+tanA+secA)

= {1+(cosA/sinA)-(1/sinA)}{1+(sinA/cosA)+(1/cosA)}

= {(sinA + cosA - 1)/sinA}{(sinA + cosA + 1)/cosA}

= {(sinA + cosA)² - 1}/sinA.cosA

= (sin²A + cos²A - 1 + 2sinA.cosA)/sinA.cosA

= (1-1+2sinA.cosA)/sinA.cosA

= 2 = RHS [proved]

That's it
Hope it helped (≧∇≦)b