ત્રિકોણમિતિય વિધયો — ગણિત ધોરણ 11 સાયન્સ — Question

$P_n = cos^nx + sin^nx$

$P_6 = cos^6 x + sin^6 x$

$= \left(cos^2x + sin^2x\right) \ \left(cos^4x + sin^4x - cos^2x \ sin^2 x\right)$

$= \left(\left(cos^2x + sin^2x\right)^2 - 3sin^2x \ cos^2 x\right)(1)$

$P_6 = 1 - 3 sin^2x \ cos^2 x$

$P_4 = cos^4x + sin^4 x$

$P_4 = 1 - 2sin^2x \ cos^2x$

$3P_4 - 2P_6 = 3 - 6sin^2x \ cos^2 x - 2 + 6 sin^2 x \ cos^2 x$

$3P_4 - 2P_6 = 1$