If `s e c(x+alpha)+s e c(x-alpha)=2 s e c x ,` prove that `cos x = +- sqrt2 cos (alpha/2)`

If x sin alpha = y cos alpha, prove that : x/(sec 2alpha) + y/(cosec 2 alpha) = x

(cos2 x - cos2 alpha)/(cos x - cos alpha)

If x sin alpha=y cos alpha, prove that :(x)/(sec2 alpha)+(y)/(cos ec2 alpha)=x

(cos2x-cos2 alpha)/(cos x-cos alpha)

(cos2x-cos2 alpha)/(cos x-cos alpha)

For alpha=pi/7 which of the following hold(s) good? (a) tanalphatan2alphatan3alpha=tan3alpha-tan2alpha-tanalpha (b) cos e calpha=cos e c2alpha+cos e c4alpha (c) cosalpha-cos2alpha+cos3alpha=1/2 (d) 8cosalphacos2alphacos4alpha=1

If s in alpha+s in beta=a and cos alpha+cos beta=b prove that: cos(alpha-beta=(a^(2)+b^(2)-2)/(2))

For alpha=pi/7 which of the following hold(s) good? (a) tanalphatan2alphatan3alpha=tan3alpha-tan2alpha-tanalpha (b)cos e calpha=cos e c2alpha+cos e c4alpha (c)cosalpha-cos2alpha+cos3alpha=1/2 (d)8cosalphacos2alphacos4alpha=1

Let lambda and alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+ (sin alpha) y + (cos alpha)z = 0 , x + (cos alpha) y + (sin alpha) z = 0 , -x + (sin alpha) y - (cos alpha) z = 0 has a non trivial solution then S contains a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]

If tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prove that cos beta = ( cos alpha - e )/( 1 - e cos alpha ).