Given tan(pi cosx) = cot(pi sinx) then value of cos(x-1/4pi) will be: a. 1/2root2 b. 1/root2 c. 1/3 root2 d. 1/4root2
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tan(πcosx)=cot(πsinx)
or, tan(πcosx)=tan(π/2-πsinx) [∵, tan(π/2+Ф)=cotФ]
or, πcosx=π/2-πsinx
or, π(sinx+cosx)=π/2
or, sinx+cosx=1/2
or, (sinx+cosx)1/√2=1/2√2
or, cosx(1/√2)+sinx(1/√2)=1/2√2
or, cosxcosπ/4+sinxsinπ/4=1/2√2
or, cos(x-π/4)=1/2√2
∴, a)1/2√2 is the right answer.
or, tan(πcosx)=tan(π/2-πsinx) [∵, tan(π/2+Ф)=cotФ]
or, πcosx=π/2-πsinx
or, π(sinx+cosx)=π/2
or, sinx+cosx=1/2
or, (sinx+cosx)1/√2=1/2√2
or, cosx(1/√2)+sinx(1/√2)=1/2√2
or, cosxcosπ/4+sinxsinπ/4=1/2√2
or, cos(x-π/4)=1/2√2
∴, a)1/2√2 is the right answer.
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