Question

Verify the identity. cot. (x - (pi/2)) = -tan xPlease, help me!!!

Answer 1

Answer:

cot . (x- π/2)= - tanx

Step-by-step explanation:

cot . (x- π/2)= - tanx

cot .x - cot π/2= - tanx

cot π/2= 1/tanπ/2

But tan π/2= ∞

cot π/2 = 1/∞= 0

cotx - 0= - tanx

cot x = - tanx

cosx/sinx= - sinx/cosx             Putting values of cot and tan

cosx/ sinx ( sinx/cos x) = -sinx/cos x  (sinx/cos x )  

Multiplying both sides with  sinx/cos x    

1= - sin²x/cos²x

cos²x= - sin²x                 as cosx = -sinx