0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Prove that tan(π4+θ2)=1secθtanθ

Solution
Verified by Toppr

Given: tan(π4+θ2)
We know, tan(A+B)=tanA+tanB1tanAtanB
tan(π4+θ2)=tanπ4+tanθ21tanπ4+tanθ2=1+tanθ21tanθ2
=cosθ2+sinθ2cosθ2sinθ2
Multiply denominator to numerator by 2cosθ2
2cos2θ2+2sinθ2cosθ22cos2θ22sinθ2cosθ2

1+cosθ+sinθ1+cosθsinθ×1+cosθ+sinθ1+cosθ+sinθ

(1+2cosθ2sinθ2)cosθ2cosθcosθ2

1+sinθcosθ
secθ+tanθ×secθtanθsecθ+tanθ
1secθtanθ

1049000_1177787_ans_ba679697ef1f4754a9f7119091bb757b.png

Was this answer helpful?
1
Similar Questions
Q1
Prove that tan(π4+θ2)=1secθtanθ
View Solution
Q2
Prove that tan(π4+θ)tan(π4θ)=2tan2θ
View Solution
Q3
Prove that
tan(π4+θ)+tan(π4θ)=2sec2θ
View Solution
Q4
Prove the following :
tan(π4+θ)=1+tanθ1tanθ
View Solution
Q5
Prove that :
1secθtanθ=secθ+tanθ
View Solution