Sunday, 30 April 2017

algebra precalculus - If tan(picostheta)=cot(pisintheta) then find the value of cosleft(thetafracpi4right)




If tan(πcosθ)=cot(πsinθ) then find the value of cos(θπ4).



I could not get any idea to solve. However I tried by using θ=0. But could not get the answer.


Answer



Hint -



tan(πcosθ)=cot(πsinθ)



tan(πcosθ)=tan(π2πsinθ)




πcosθ=π2πsinθ



cosθ=12sinθ



sinθ+cosθ=12



Now we have,



cos(θπ4)




=cosθcosπ4+sinθsinπ4



=cosθ12+sinθ12



=12(cosθ+sinθ)



=12(12)



=122


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