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If 3sintheta+5costheta=5, then show tha...

If `3sintheta+5costheta=5,` then show that `5sintheta-3costheta=+-3.`

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Given 3sinθ+5cosθ=5 Let 5sinθ−3cosθ=x
Squaring on both sides for both the equations
`⇒9sin2θ+25cos2θ+30sinθcosθ=25`
...
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. If cos e ctheta-sintheta=a^3,sectheta-costheta=b^3, Prove that : a^2b...

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  2. If acos^2theta+3acosthetas in^2theta=ma n das in^3theta+3acos^2thetas ...

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  3. If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

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  4. If acostheta+bsintheta=m and asintheta-bcostheta=n , Prove that a^2...

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  5. If costheta+cos^2theta=1, Prove that: sin^(12)theta+3sin^(10)theta+3si...

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  6. If cottheta=15/8, then Evaluate ((2+2sintheta)(1-sintheta))/((1+costhe...

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  7. Prove the trigonometric identities: (tantheta)/(1-cottheta)+(cottheta)...

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  8. If sintheta+costheta=x , Prove that : sin^6theta+cos^6theta=(4-3(x^2-1...

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  9. Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(co...

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  10. Prove that (1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)

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  11. Prove the following identities: (sinA+secA)^2+(cos"A"+"c o s e cA")^2=...

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  12. Prove the following identities: (1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2...

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  13. Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+...

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  14. Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bc...

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  15. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

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  16. If tantheta+sintheta=m and tantheta-sintheta=n , then m^2-n^2=

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  17. if (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB) (secC-t...

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  18. Prove the following identities: (cosA)/(1-sinA)+(sinA)/(1-cosA)+1 = (...

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  19. If tan^2theta=1-a^2, prove thats e ctheta+tan^3thetacos e ctheta=(2-a^...

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  20. If a sectheta+bt a ntheta+c=0 and psectheta+qtantheta+r=0, prove that...

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