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`(sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta`

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Given,`(sintheta +sin2theta)/(1+costheta+cos2theta)`
=`(sintheta +2sinthetacostheta)/(1+costheta+2cos^2theta-1)`
=`[sintheta(1+2costheta)]/[(costheta(1+2costheta}]`
=`tantheta`
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: \ sqrt(2+sqrt(2+2cos4theta))=2costheta

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  2. (1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

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  3. (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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  4. Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

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  5. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

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  6. Prove that: sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

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  7. Prove that: (cosalpha+cosbeta)^2+(s inalpha+s inbeta)^2=4cos^2\ \ ((al...

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  8. Prove that: 1+cos^2 2x=2(cos^4x+sin^4x)

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  9. cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

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  10. Prove that : (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

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  11. Prove that:cos^2(pi/4-theta)-sin^2(pi/4-theta)=s in2theta

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  12. Prove that: cos4A=1-8cos^2A+8cos^4 A

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  13. Prove that 3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13

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  14. cos^6A-sin^6A=cos2A(1-1/4sin^2 2A)

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  15. Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta .

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  16. Prove that: cot^2A-tan^2A=4 cot2A cosec2A

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  17. sin4A=4sinAcos^3A-4cosAsin^3A

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  18. Prove that: \ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2

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