Question

(cotA/cotA-cot3A)-(tanA/tan3A-tanA)=1​

Answer 1

$\textbf{To prove:}$

$\dfrac{cotA}{cotA-cot3A}-\dfrac{tanA}{tan3A-tanA}=1$

$\text{Consider,}$

$\dfrac{cotA}{cotA-cot3A}-\dfrac{tanA}{tan3A-tanA}$

$=\dfrac{\frac{1}{tanA}}{\frac{1}{tanA}-\frac{1}{tan3A}}-\dfrac{tanA}{tan3A-tanA}$

$=\dfrac{\frac{1}{tanA}}{\frac{tan3A-tanA}{tanA\;tan3A}}-\dfrac{tanA}{tan3A-tanA}$

$=\dfrac{\frac{tanA\;tan3A}{tanA}}{tan3A-tanA}-\dfrac{tanA}{tan3A-tanA}$

$=\dfrac{tan3A}{tan3A-tanA}-\dfrac{tanA}{tan3A-tanA}$

$=\dfrac{tan3A-tanA}{tan3A-tanA}$

$=1$

$\therefore\boxed{\bf\dfrac{cotA}{cotA-cot3A}-\dfrac{tanA}{tan3A-tanA}=1}$

Find more:

Prove that (tanA + secA ÷ cosecA + cotA)(tanA - secA ÷ cosecA - cotA) = 2(tanA×cosecA - cotA×secA)

https://brainly.in/question/8676527

Answer 2

Answer:

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