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Prove the trigonometric identities: (1-...

Prove the trigonometric identities: `(1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2`

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LHS=`(1-sin theta)/(1+ sin theta)`
On multypling by its conjugate, we have
`(1-sin theta)/(1+sin theta) X (1-sin theta)/(1-sin theta)`
since, `1-sin^2 theta = cos^2 theta`
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
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  2. Without using trigonometric tables, evaluate each of the following: (...

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  3. Prove the trigonometric identities: (1-sintheta)/(1+sintheta)=(secthe...

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  4. Prove the trigonometric identities: sqrt((1-costheta)/(1+costheta))=co...

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  5. If sectheta=x+1/(4x) ,prove that :sectheta+tantheta=2xor ,1/(2x)

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  6. Prove that : (sinthetacos(90^0-theta)costheta)/(sin(90^0-theta))+(cost...

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  7. If sectheta+tantheta=x , obtain the values of sectheta,t a ntheta and...

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  8. If sintheta+sin^2theta=1,find the value of cos^(12)theta+3cos^(10)t...

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  9. If sintheta+sin^2theta+sin^3theta=1, then prove that cos^6theta-4cos^4...

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  10. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

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  11. If acostheta-bsintheta=c, then prove that: asintheta+bcostheta=+-sqr...

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  12. Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+s...

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  13. Prove the following identities: (sintheta)/(1-costheta)+(tantheta)/(1...

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  14. Find (1 + tantheta + sectheta)(1+ cottheta - cosectheta)

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  15. Prove the following identities: 1/(cos e cA-cotA)-1/(sinA)=1/(sinA)-1/...

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  16. Prove the following trigonometric identities: (sintheta)/(1-costheta)=...

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  17. Prove the following trigonometric identities: sqrt((1-sintheta)/(1+sin...

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  18. Prove the following identities: (1-sintheta)/(1+sintheta)= (sectheta...

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  19. If cos e ctheta-sintheta=l and sectheta-costheta=m , prove that l^2m^2...

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  20. If tanA=ntanB and sinA=msinB, prove that cos^2A=[m^2-1]/[n^2-1]

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