# If m sin theta+r cos theta=p and m cos theta-n sin theta=q,then prove that m^2+n^2=p^2+p^2

1
by Sreemath

Log in to add a comment

by Sreemath

Log in to add a comment

The Brainliest Answer!

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

M Sin Ф + n Cos Ф = p

=> m² Sin² Ф + n² Cos² Ф + 2 m n Sin Ф Cos Ф = p²

m Cos Ф - n Sin Ф = q

=> m² Cos² Ф + n² Sin²Ф - 2 m n Sin Ф Cos Ф = q²

add the two equations:

m² (sin²Ф +Cos²Ф) + n²(sin²Ф+Cos²Ф) = p² + q²

m² + n² = p² + q²

=> m² Sin² Ф + n² Cos² Ф + 2 m n Sin Ф Cos Ф = p²

m Cos Ф - n Sin Ф = q

=> m² Cos² Ф + n² Sin²Ф - 2 m n Sin Ф Cos Ф = q²

add the two equations:

m² (sin²Ф +Cos²Ф) + n²(sin²Ф+Cos²Ф) = p² + q²

m² + n² = p² + q²