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Prove the following identities: (1+sec...

Prove the following identities:
`(1+secA+tanA)(1-cosecA+cotA)=2`

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Prove the following identities: sqrt((cosectheta-1)/(cosec+1))=(1-sintheta)/(costheta)

Prove the following identities: sqrt((1+sintheta)/(1-sin theta))=sectheta+tantheta

Prove the following identities: (sec theta-tan theta+1)/(sec theta+tantheta+1)=(1-sin theta)/(cos theta)

Prove the following identities: sqrt((1-cos theta)/(1+cos theta))-cosec theta=cosec theta-sqrt((1+cos theta)/(1-cos theta))

Prove the following identities: (cosec theta-sintheta)^2+(sectheta-costheta)^2-(tantheta-cottheta)^2=1

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. Prove the following identities: (1+sintheta)/(1-sintheta)=(sectheta+...

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  2. Prove the following identities: (sinalpha+cosecalpha)^2+(cosalpha+se...

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  3. Prove the following identities: (1+secA+tanA)(1-cosecA+cotA)=2

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  4. prove: ((sin0^@+sin60^@)(cos60^@+cot45^@))/((cot60^@+tan30^@)(cosec30^...

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  5. prove: cos^2 ""60^@,cos^2 ""45^@,cos^2 ""30^@ are in A.P

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  6. prove: tan(pi/3),tan(pi/4),tan(pi/6) are in G.P

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  7. prove: 2cos^2(pi/3)+3/4sec^2(pi/4)+4sin^2(pi/6)=cot^2(pi/6)

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  8. The angle A of the triangle ABC is obtuse, if sec(B+C)=cosec (B-C)=2,...

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  9. If theta is a positive acute angle and tan theta=3/4, find sin theta...

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  10. If theta is a positive acute angle and sec theta =(m^2+1)/(2m) find ...

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  11. If theta is a positive acute angle and cos theta=(15)/(17) , find th...

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  12. If A and B are positive acute angles and sinA =3/5,cosB=(15)/(17) , fi...

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  13. If tantheta =a/b, find the value of (bcostheta-asintheta)/(b cos theta...

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  14. If cos theta +sec theta=sqrt(3), show that, cos^3theta+sec^3theta=0 .

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  15. Express 1+4cosec^2alphacot^2alpha in the form of a perfect square.

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  16. If 3cos alpha-4sinalpha=5, show that, 3sinalpha+4cosalpha=0 .

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  17. If sinalpha=x and tan alpha=y, prove that, 1/x^2-1/y^2=1.

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  18. If tan alpha+cotalpha=2, show that, tan^7alpha+cot^7alpha=2.

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  19. If an=sin^n theta+cosec^ntheta and a1=2 prove that, an=2 .

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  20. If cosalpha+secalpha=2, show that cos^3alpha+sec^3alpha=2.

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