Verify the identify.\frac{\tan^2\theta}{\sec\theta+1}=\frac{1-\cos x}{\cos x}

coexpennan 2021-09-12 Answered
Verify the identify.
tan2θsecθ+1=1cosxcosx
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Expert Answer

Laith Petty
Answered 2021-09-13 Author has 103 answers
Solution:
LHS=tan2θsecθ+1
=(sinθcosθ)21cosθ+1
=sin2θcos2θ1+cosθcosθ
=sin2θcosθ(1+cosθ)
=(1cos2θ)cosθ(1+cosθ)
=(1cosθ)(1+cosθ)cosθ(1+cosθ)
=1cosθcosθ
=RHS
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Jeffrey Jordon
Answered 2022-01-31 Author has 2581 answers

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Trigonometry equation simplification
So, I've been given the trig equation:
csc 2 x cot 2 x = 1
Using the identity and rearranging
cot 2 2 x + 1 = csc 2 2 x
the equation simplifies to
cot 2 2 x cot 2 x = 0
factoring out cot 2 x
cot 2 x ( cot 2 x 1 ) = 0
I've bee told to solve x | 0 x 180
So...
cot 2 x = 0
or
cot 2 x = 1
1 tan 2 x = 0 1 = 0 × tan 2 x
therefore no solutions.
cot 2 x = 1 tan 2 x = 1
x { 22.5 , 112.5 }
Both of my solutions were correct, but I lost marks since apparently there are two extra solutions! 45 & 135 degrees. I don't know where I went wrong in my workings and was wondering if someone could tell me what I did wrong.

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