If `t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2` , prove that `costheta=(a cosvarphi+b)/(a+b cosvarphi)` .

If "tan"(theta)/(2)=sqrt((a-b)/(a+b))"tan"(varphi)/(2) , prove that cos theta =(a cosvarphi+b)/(a+bcosvarphi) .

If tantheta/2=sqrt((2-b)/(a+b))tanphi/2 , prove that cosalpha=(1cosphi+b)/(a+b cosphi)

If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a + b cos phi = (a cos phi+ b) sec theta .

If t a ntheta/2=sqrt((1-e)/(1+e))tan(alpha/2) , then cosalpha= (a) 1-ecos(costheta+e) (b) (1+ecostheta)/(costheta-e) (c) (1-ecostheta)/(costheta-e) (d) (costheta-e)/(1-ecostheta)

If tan A tan B=sqrt((a-b)/(a+b)), prove that (a-b cos2A)(a-b cos2B)=a^(2)-b^(2)

If 2costheta=a+1/a and 2 cosphi=b+1/b ,then prove that 2cos(theta-phi)=a/b+b/a

If sintheta=a/(sqrt((a^(2)+b^(2)+c^(2)+2bc))) , then show that (b+c)sintheta=(a)costheta .

Factors of cos4theta-cos4varphi are- a. (costheta+cosvarphi) b. \ (costheta-cosvarphi) c. (costheta+sinvarphi) d. (costheta-sinvarphi)

If sintheta=5sin(theta+varphi),t h e ntan(theta+varphi)= (sinvarphi)/(cosvarphi-3) b. (sinvarphi)/(cosvarphi+3) c. (sinvarphi)/(cosvarphi-5) d. (cosvarphi)/(sinvarphi+5)