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Prove the following identities: (cos a...

Prove the following identities:
`(cos alpha cos beta+sin alphasin beta)^2+(sinalphacos beta-cos alphasinbeta)^2=1`

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. Prove the following identities: sqrt((1-cos theta)/(1+cos theta))-co...

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  2. Prove the following identities: cot^2alpha(secalpha-1)/(1+sinalpha)+...

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  3. Prove the following identities: (cos alpha cos beta+sin alphasin bet...

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  4. Solve : (0^@le thetale90^@): tan theta +cot theta=2

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  5. Solve : (0^@le thetale90^@): 2cos^2 theta +5 sin theta =4

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  6. Solve : (0^@le thetale90^@): tan^2 theta-(sqrt(3)+1) tan theta+sqrt...

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  7. Solve : (0^@le thetale90^@): sec^2 theta+tan^2theta=7

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  8. Solve : (0^@le thetale90^@): 2 sin ^2theta=3(1-cos theta)

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  9. Solve : (0^@le thetale90^@): 2 sin theta tan theta +1=tan theta+2 s...

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  10. If alpha, beta, gamma ,are positive acute angles and sin (alpha+beta-g...

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  11. If A,B,C are the angles of an acute angled triangle and cos(B+C-A)=0, ...

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  12. If 1+cos^2A=3 cos AsinA, find the value of cotA.

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  13. If 3 sin theta+4cos theta=5(0lt theta lt pi/2), show that sin theta =3...

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  14. If cosecalpha+cotalpha=a, prove that , cos alpha =(a^2-1)/(a^2+1).

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  15. If 4xsec A =1+4x^2 , prove that, sec A +tan A=2xor,1/(2x).

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  16. If tan ^2theta=1-e^2 , prove that, sectheta+tan^3thetacosec theta=(2-e...

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  17. If a^2sec^2alpha-b^2tan^2alpha=c^2 show that, sinalpha=pm sqrt((c^2-a^...

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  18. If sin^4theta+sin^2 theta=1 show that, tan^4theta-tan^2theta=1 .

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  19. If tan^4theta+tan^2theta=1 , prove that, cos^4 theta+cos^2theta=1

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  20. If sin^2theta=cos^3theta prove that, cot^6theta-cot^2theta=1 .

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