(solved)Question 8 SSC-CGL 2020 March 3 Shift 1

Question 8
SSC-CGL 2020 Mar 3 Shift 1

if x = 4cos A + 5sin A, and y = 4sin A - 5cos A, then find the value of (x² + y²)?

Solution

Squaring $\displaystyle x = 4\cos A + 5\sin A$,

$ \begin{aligned} x^2 = &16 \cos^2 A + 25 \sin^2 A \\ &+ 40 \cos A \sin A \text{ . . . (1)} \end{aligned} $

Squaring $\displaystyle y = 4\sin A + 5\cos A$,

$ \begin{aligned} y^2 = &16 \sin^2 A + 25 \cos^2 A \\ &- 40 \cos A \sin A \text{ . . . (2)} \end{aligned} $

Adding (1) and (2), we get

$ \begin{aligned} x^2 + y^2 = &16 (\cos^2 A + \sin^2 A) \\ &+ 25 (\sin^2 A + \cos^2 A) \\ \end{aligned} $

which is $\displaystyle = 16 + 25 = 41 \:\underline{ Ans}$