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Prove that : cos^2alpha+cos^2(alpha+beta...

Prove that : `cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta`

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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Solve the inequality: log(1//2)(x+1) gt log(2)(2-x)

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  2. Solve the inequality: log(x)2.log(2x)2. log(2)4x gt 1

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  3. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

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  4. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  5. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

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  6. If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot...

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  7. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

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  8. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

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  9. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

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  10. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  11. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  12. Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7).

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  13. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  14. Calculate without using trigonometric tables: (a) 4 cos 20^@ - sqrt3 c...

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  15. (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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  16. cos^6(pi/16)+cos^6(3pi/16)+cos^6(5pi/16)+cos^6(7pi/16)

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  17. tan1 0^(@)-tan5 0^(@)+tan7 0^(@)

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  18. Given that (1+tan1^@)(1+tan2^@)+...........+(1+tan45^@)= 2^n find n .

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  19. If a leq 3 cos (theta+pi/3)+5cos theta+3 leq b, find a and b, where ...

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  20. Let k=1^@ then prove that sum(n=0)^(88)1/(cosnkcos(n+1)k)=cosk/sin^2k

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