Math
posted by Lucia .
How can I prove this identity?
(1 + sinØ + cosØ):(1  sinØ + cosØ) =
(1 + sinØ) : cosØ

Work on the left hand side:
(1 + sinØ + cosØ)/(1  sinØ + cosØ)
multiply both the numerator and denominator by (1sinφ+cosφ) and simplify:
((1+cosφ)^2sin&hi;^2)/(1sinφ+cosφ)^2
=2cosφ(1+cosφ)/[2(1sinφ)(1+cosφ)]
=2cosφ/[2(1sinφ)]
=cosφ/(1sinφ)
Now multiply top and bottom by (1+sinφ)
cosφ(1+sinφ)/(1sin²φ)
=cosφ(1+sinφ)/cos²φ
=(1+sinφ)/cosφ
Respond to this Question
Similar Questions

trig
how do you solve this problem? 1+sinØ/cosØ +cosØ/1+sinØ = 2secØ and cosß cosß/1tanß = sinßcosß/sinßcosß 
Algebra 2
As the answer to: (tanØ * cosØ/ sinØ) + cotØ * sinØ * tanØ* cscØ I got 2, is that correct? 
maths
if sinØ=cosØ then find the value of Ø 
math
Two sides of a triangle have lengths 8 m and 24 m. The angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is 135°. … 
Advanced Functions/Precalculus
1. The expression sinπ is equal to 0, while the expression 1/cscπ is undefined. Why is sinø=1/cscø still an identity? 
Trig
Prove the following: 1/(tanØ  secØ ) + 1/(tanØ + secØ) = 2tanØ (1  sinØ)/(1 + sinØ) = sec^2Ø  2secØtanØ + tan^2Ø 
Algebra 2
Verify the identity , justify each step tanØ+cotØ = 1/ sin Ø cosØ 
Math
If cscØ = 4/3, find sinØ + sinØ cot^2 Ø 
Math
If cscØ = 4/3, find sinØ + sinØ cot^2 Ø 
Maths
Prove that:Tanø+sinø/tanøsinø=secø+1/secø1