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Prove that: (cos(pi+x)cos(-x))/(sin(pi-x...

Prove that: `(cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)` = `cot^2x`

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To prove that \[ \frac{\cos(\pi + x) \cos(-x)}{\sin(\pi - x) \cos\left(\frac{\pi}{2} + x\right)} = \cot^2 x, \] we will simplify the left-hand side step by step. ...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove that: sqrt((1-sintheta)/(1+sintheta))+sqrt((1+sintheta)/(1-sinth...

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  2. Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

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  3. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x) = cot^2x

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  4. If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+...

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  5. If tanx=(b)/(a), then find the value of sqrt((a+b)/( a-b ))+sqrt((a-b)...

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  6. Find the values of the following trigonometric ratios. (i)cosec390^0 ...

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  7. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

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  8. Prove that: "sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+the...

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  9. Find the value of : sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2...

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  10. If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A...

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  11. Find the value of the expression 3{sin^4((3pi)/2-theta)+sin^4(3pi+the...

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  12. If t a n^2theta=1-a^2 , prove that sectheta+t a n^3thetacos e ctheta=...

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  13. If acos^2theta+3acostheta sin^2theta=m and asin^3theta+3acos^2thetasin...

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  14. If 2t a n^2alphat a n^2betat a n^2gamma+t a n^2alphat a n^2beta+t a ...

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  15. If m^2 + m'^2 + 2mm' costheta = 1 and n^2+n'^2+2n n'costheta=1, (mn +...

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  16. If (sin^4theta)/a+(cos^4theta)/b=1/(a+b) , prove that (sin^8theta)/...

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  17. If (cos^4alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 prove that (i...

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  18. If x is any non-zero real number, show that costheta' a n d ' sinthet...

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  19. If A=cos^2theta+sin^4theta, prove that 3/4lt=Alt=1 for all values of...

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  20. If tantheta+sectheta=e^x then costheta equals

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