If `a sinalpha+bcosalpha=c` and `a cosecalpha+bsecalpha=c` show that`sin2alpha=(2ab)/(c^2-a^2-b^2)`

"If " a sin theta + b cos theta = c " and " a cosec theta + b sec theta = c "show that ," sin 2 theta=(2ab)/(c^(2)-a^(2)-b^(2))

If 0ltalphaltpi/2 and sinalpha+cosalpha+tanalpha+cotalpha+secalpha+cosecalpha="7, then prove that sin2alpha is a root of the equation x^2-44x-36=0.

If cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .

if tan theta=(sinalpha-cosalpha)/(sinalpha+cosalpha) show that, sin alpha+cosalpha=pmsqrt(2)cos theta

If alpha and beta be two roots of the equation a cos theta+ b sin theta=c , show that sin alpha+ sin beta=(2bc)/(a^(2)+b^(2)) ,sin alpha sin beta =(c^(2)-a^(2))/(a^(2)+b^(2)) and tan (alpha+ beta)=(2ab)/(a^(2)-b^(2))

If alpha, beta are the solutions of the equation a tantheta+b sectheta=c then show that tan(alpha+beta)=(2ac)/(a^2-c^2 .

(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a) sec(alpha/2-pi/8) (b) cos(pi/8-alpha/2) (c) tan(alpha/2-pi/8) (d) cot(alpha/2-pi/2)

If angles alpha and beta satisfy the equation a cos theta+ b sin theta= c(a,b,c are constants), prove that- (a) sin (alpha+ beta)= (2ab)/(a^(2)+b^(2)) (b) cos (alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2)) (c) cos (alpha- beta)=(2c^(2)-(a^(2)+b^(2)))/(a^(2)+b^(2))

If " "a cos theta + b sin theta =c " and " b cosec theta - a sec theta = c, " prove that" cot 2 theta = (c^(2) + a^(2) - b^(2))/(2ab)

If sin alpha=(a^(2)-b^(2))/(a^(2)+b^(2)) , then show that cot alpha=(2ab)/(a^(2)-b^(2)) .