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Trigonometric Equations

If tan A + A ...

Question

If tan A +cot A =4, then the value of $t a n^{4} A + c o t^{4} A .$

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Solution

$(t a n A + c o t A)^{2} = t a n^{2} A + c o t^{2} A + 2 t a n A c o t A$

$16 = t a n^{2} A + c o t^{2} A + 2$

$t a n^{2} A + c o t^{2} A = 14$

$(t a n A + c o t A)^{4} = t a n^{4} A + 4 t a n^{3} A c o t A + 6 t a n^{2} A c o t^{2} A + 4 t a n A c o t^{3} A + c o t^{4} A$

$256 == t a n^{4} A + 4 (t a n^{2} A + c o t^{2} A) + c o t^{4} A + 6$

$256 = t a n^{4} A + 4 (14) + c o t^{4} A + 6$

$t a n^{4} A + c o t^{4} A = 194$

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Similar questions

Q. If tan A + cot A = 4, then write the value of tan⁴ A + cot⁴ A.

Q. If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to
(a) 110
(b) 191
(c) 80
(d) 194

If tan A +cot A =4, then $t a n^{4} A + c o t^{4} A$ is equal to

\sqrt{2} cos A = 1

then the value of

{tan}^{4} A + {cot}^{4} A

{tan}^{3} A + {cot}^{3} A = 18

, then the value of

{tan}^{4} A + {cot}^{4} A - 40

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