જો a cos^3 α + 3a ,cos, α , sin^2, α = m અને asin^3, α + 3a , cos^2, α ,sin, α = n ?

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3.Trigonometrical Ratios, Functions and Identities

hard

જો a $cos^3 \alpha + 3a \,cos\, \alpha \, sin^2\, \alpha = m$અને $asin^3\, \alpha + 3a \, cos^2\, \alpha \,sin\, \alpha = n$ હોય તો $(m + n)^{2/3} + (m - n)^{2/3}$ =

$2\, a^2$

$2\, a^{1/3}$

$2 \,a^{2/3}$

$2\, a^3$

Add $-$ raise to the power $2/3$ ; subtract $-$ raise to the power $2/3$ & add the two results ]

$m+n = a\{(cos^3\alpha + sin^3\alpha ) + 3\, cos\alpha \,sin\alpha \,(cos\alpha + sin\alpha ) \}$

$m+n = a \{cos\alpha + sin\alpha \}^3$

$|||^{1y}$ $m-n = a\{cos\alpha – sin\alpha \}^3$

$(m+n)^{2/3} = a^{2/3} (cos\alpha + sin\alpha )^2$

add. $(m-n)^{2/3} = a^{2/3}(cos\alpha -sin\alpha)^2$

________________________

$= a^{2/3}$ $(2)$ $\Rightarrow$ $2a^{2/3}$

Standard 11

Mathematics

medium

medium

medium

medium

medium