Home
Class 12
MATHS
Prove that tan phi/(1-cot phi)+cot phi/(...

Prove that `tan phi/(1-cot phi)+cot phi/(1-tan phi)=1+tan phi+cot phi`

Text Solution

Verified by Experts

LHS=`tan phi/(1 - 1/tan phi) + (1/ tan phi)/(1 - tan phi)`
`= tan^2 phi/(tan phi -1) + 1/(tan phi(1-tan phi))`
`= tan^2 phi/(tan phi - 1) - 1/(tan phi (tan phi - 1))`
`= (tan^3 phi - 1)/((tan phi -1)tan phi)`
`= ((tan phi -1)(tan^2 phi + tan phi + 1))/(tan phi (tan phi - 1))`
`= tan phi + 1 + cot phi`
hence proved
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that sin^(2)phi(1+cot^(2)phi)=1

tan phi cos ec phi=sec phi

The value of (sec phi(1-sin phi)(sin phi+cos phi) (sec phi+tan phi))/(sin phi(1+tan phi)+cos phi(1+ cot phi)) is equal to :

phi is an acute angle such that tan phi=(2)/(3) then evaluate ((1+tan phi)/(sin phi+cos phi))*((1-cot phi)/(sec phi+csc phi ))

The value of sqrt((cosec phi-cot phi)/(cosec phi +cot phi)) div (sin phi)/(1+cos phi) is equal to:

Prove that : (sin (x+theta))/(sin (x+phi))= cos (theta-phi)+ cot (x+phi)sin(theta-phi) .

If x=sec phi-tan phi and y=cos ec phi+cot phi then

int(tan phi+tan^(3)phi)/(1+tan^(3)phi)d phi

Prove that, "cosec" (theta + phi)=("cosec" theta "cosec" phi)/(cot theta + cot phi)

If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (tan^(2) alpha sin 2 phi)/(1+ tan^(2) alpha cos 2 phi)