+91-87964 74404
FlagBACK
Question icon
Grade 12Trigonometry

If sin(piecosx)=cos(piesinx)? Find x? please

Profile image of Abhishek
8 Years agoGrade 12
Answers icon

1 Answer

Profile image of Sujit Kumar
8 Years ago
My solution to this question is given bellow.
sin(\pi cosx)=cos(\pi sinx)
\rightarrow sin(\pi cosx)=sin(\frac{\pi}{2} - \pi sinx)
\rightarrow \pi cosx=\frac{\pi}{2} - \pi sinx
\rightarrow cosx=\frac{1}{2} - sinx
\rightarrow sinx=\frac{1}{2} - (1-sin^{2}x)^{\frac{1}{2}}
\rightarrow (1-sin^{2}x)^{\frac{1}{2}}=\frac{1}{2} - sinx
SQUARING ON BOTH SIDES
\rightarrow (1-sin^{2}x)=\frac{1}{4} - sinx + sin^{2}x
\rightarrow 2sin^{2}x - sinx-\frac{3}{4}=0
\rightarrow 8sin^{2}x - 4sinx-3=0
SOLVING THE QUADRATIC EQUATION
\rightarrow sinx=\frac{4\pm (16+96)^{\frac{1}{2}}}{16}
\rightarrow sinx=\frac{1\pm (7)^{\frac{1}{2}}}{4}
\rightarrow x=sin^{-1}(\frac{1\pm (7)^{\frac{1}{2}}}{4})
This is the value of x according to me.

Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥 
trigonometry
1 Answer Available

Last Activity: 4 Years ago