What is the best way to find the ncert class 10 question of trigonometry in a simplest and easiest way . Please help me to find the best solution of exercise 8.4of the trigonometry . Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(x) (1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A.
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Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(x) (1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A. Q.5(10)
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(1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A
L.H.S. = (1+tan2A/1+cot2A)
Since cot function is the inverse of tan function,
= (1+tan2A/1+1/tan2A)
= 1+tan2A/[(1+tan2A)/tan2A]
Now cancel the 1+tan2A terms, we get
= tan2A
(1+tan2A/1+cot2A) = tan2A
Similarly,
(1-tan A/1-cot A)2 = tan2A
Hence proved