Question

if tan theta + cot theta = 4, find tan theta is to 4 + cot theta is to 4​

Answer 1

Answer:

your answer is 5 letter bite

Answer 2

Given:-

• tanθ + cotθ = 4

To Find:-

• The value of tan⁴θ + cot⁴θ

Solution:-

We are given:- tanθ + cotθ = 4

$\qquad\small\underline{\pmb{\sf \:Squaring \: on \: both \: sides :-}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ \big( tanθ + cotθ \big) ² = 4²}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan²θ + cot²θ + 2tanθcotθ = 16}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan²θ + cot²θ + 2 × tanθ × \dfrac{1}{tanθ }= 16}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan²θ + cot²θ + 2 = 16}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan²θ + cot²θ = 16 - 2}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan²θ + cot²θ = 14}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ \big( tan²θ + cot²θ \big) ² = \big( 14 \big)²}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan⁴θ + cot⁴θ + 2tan²θcot²θ = 196}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan⁴θ + cot⁴θ + 2 × tan²θ × \dfrac{1}{tan²θ} = 196}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan⁴θ + cot⁴θ + 2 = 196}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ tan⁴θ + cot⁴θ = 196 - 2}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ tan⁴θ + cot⁴θ = 194}}}$

• Therefore the value of tan⁴θ + cot⁴θ is 194.

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