Question

If (1+sina)(1+sinb)(1+sinc)=(1-sina)(1-sinb)(1-sinc)=k then value of k=?

a. (cosacosbcosc)
b.(sinasinbsinc)
c. (3sinasinbsinc),

Answer 1

k = (1+sina)(1+sinb)(1+sinc) = (1-sina)(1-sinb)(1-sinc) Multiply both entities, k x k = (1+sina)(1+sinb)(1+sinc) x (1-sina)(1-sinb)(1-sinc) That gives k^2 = (1 - sin^2a)(1 - sin^2b)(1 - sin^2c) k^2 = (cos^2a) x (cos^2b) x (cos^2c) k = sqrt ((cos^2a) x (cos^2b) x (cos^2c)) k = cosacosbcosc option a is correct.