Question

Proove that

Given tan ( πcos¢ ) = cot ( π sin¢) then Proove that cos ( ¢ - π/4 ) = +-1/2√2

Answer 1

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Answer 2

tan(πcosθ)=cot(πsinθ)tan⁡(πcos⁡θ)=cot⁡(πsin⁡θ)

⇒tan(πcosθ)=tan{π2−(πsinθ)}⇒tan⁡(πcos⁡θ)=tan⁡{π2−(πsin⁡θ)}
⇒πcosθ=π2−(πsinθ)⇒πcos⁡θ=π2−(πsin⁡θ)
⇒12=12√[sinπ4cosθ+cosπ4sinθ]⇒12=12[sin⁡π4cos⁡θ+cos⁡π4sin⁡θ]
⇒12√=sin(π4+θ)⇒12=sin⁡(π4+θ) ⇒π4=π4+θ⇒π4=π4+θ
⇒θ=0⇒θ=0
=
∴cos(θ−π4)∴cos⁡(θ−π4) == 12√12

⇒12=2–√[sinπ4cosθ+cosπ4sinθ]⇒12=2[sinπ4cosθ+cosπ4sinθ]. –


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