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tantheta+costheta=2sin 2 theta+2cos 2 ​theta then find tan 4 theta+cot 4 theta

tantheta+costheta=2sin2theta+2cos2​theta then find tan4theta+cot4theta

Grade:10

1 Answers

Soumendu Majumdar
159 Points
3 years ago
Dear Student,
tan\theta + cot \theta = 2       since sin^2\theta + cos^2\theta =1
\Rightarrow sec\theta cosec\theta = 2
\Rightarrow 2sin\theta cos\theta = 1
\Rightarrow 2sin2\theta = 1 = sin 90^{\circ}    since sin 2A = 2sin A cos A
\Rightarrow \theta= 45^{\circ}
\Rightarrow tan^4\theta+cot^4\theta= tan^445^{\circ} + cot^445^{\circ}
=2        since   tan 45^{\circ} = cot45 ^{\circ} = 1
Hope it helps!
with regards,
Soumendu
P.S-If you have any confusion in understanding feel free to ask, I’ll be glad to help you!

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