Question

if a sin square theta + b cos square theta equal to m , b sin square alpha + cos square theta equal to n and a tan theta equal to b tan alpha prove that 1 ÷ n + 1 ÷ m equal to 1 ÷ a + 1 ÷ b

Answer 1

given: sin^2+cos^2=m

b sin^2α+cos^2=n

tan=b tanα

prove: 1/n +1/m=1/a +1/b

=1/b sin^2α+cos^2+1/sin^2+cos^2

=sin^2+cos^2 + α (b sin^2α+cos^2)/sin^2+cos^2 * sin^2α+cos^2

=sin^2+cos^2 + α /(sin^2+cos^2)sin^2α+cos^2

=sin^2+cos^2 + α / sin^2α+cos^2

=sin^2/cos^2 +sin^2/cos^2

=tan^2+btanα^2

hence proved.