Prove that from the equality `(sin^(4)alpha)/a+(cos^(4)alpha)/b=1/(a+b)` follows the relations, `(sin^(8)alpha)/a^(3) +(cos^(8)alpha)/b^(3)=1/(a+b)^(3)`

If alpha satisfies 15 sin^(4)alpha + 10 cos^(4)alpha=6 , then find the value of 27 sin^(8)alpha + 8 cos^(8) alpha

Show that : sin^6 alpha+ cos^6 alpha ge 1/4

If 15 sin^(4)alpha+10cos^(4)alpha=6 , then the value of 8 cosec^(6)alpha+27 sec^(6)alpha is

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

Prove that sinalpha*sin(60-alpha)sin(60+alpha) = 1/4*sin3alpha

cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha.

find the value of (cos^3alpha+sin^3alpha)/(1-sin(alpha).cos(alpha))

Prove that cos 4theta–cos 4alpha = 8(cos theta-cos alpha)(cos theta+ cos alpha )(cos theta -sin alpha)(cos theta+sin alpha)

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1