(1+tan2A/1+cot2a) = (1-tanA/1-cotA)2 = tan2A
Answers
Step-by-step explanation:
- Prove that
- We will firstly prove the LHS equal to the RHS and then we will be proving the middle term equal to the RHS.
: ➝ LHS :
[because we know that tan A = sin A /cos A and cot A = cos A / sin A ]
Now, taking the LCM we have
Now, as cos^2 A + sin^2 A is common in both the numerator and the denominator, they both will be cancelled out.
Now,
[because sin^2 A / cos^2 A = tan^2 A ]
= RHS
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: ➝ Middle side :
[because we know that tan A = sin A /cos A and cot A = cos A / sin A ]
Taking the LCM we have
Now, to make sin A - cos A and cos A - sin A equal we will take out -1 and as the whole equation is going to be squared -1 will also be squared:
[because sin^2 A / cos^2 A = tan^2 A ].
= RHS
□ Hence, proved.
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