The expression 3-sin 43 -2-sin 43 -2-sin 6-2-sin 65 - is equal to

The correct option is A 1 3 [sin^4 ( 3π/2 α )+ sin^4(3π+α ) ] 2 [ sin^6 ( π/2+α ) + sin^6(5 π +α ) ] =3 [cos ^4 α +sin ^4 α ] 2 [cos ^ 6 α +sin ^6 α ] = ...

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Byju's Answer

Standard XII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

The expressio...

Question

The expression $3 [{sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π + α)]$ is equal to

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$sin 4 α + cos 6 α$

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Solution

The correct option is B
1

$3 [{sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π + α)]$

$= 3 [{cos}^{4} α + {sin}^{4} α] - 2 [{cos}^{6} α + {sin}^{6} α]$

$= 3 {cos}^{4} α + 3 {sin}^{4} α - 2 {cos}^{4} α (1 - {sin}^{2} α) - 2 {sin}^{4} α (1 - {cos}^{4} α)$

$= {sin}^{4} α + {cos}^{4} α + 2 {cos}^{4} α {sin}^{2} α + 2 {sin}^{4} α {cos}^{2} α$

$= ({sin}^{2} α + {cos}^{2} α)^{2} - 2 {sin}^{2} α {cos}^{2} α + 2 {cos}^{2} α {sin}^{2} α ({cos}^{2} α + {sin}^{2} α)$

$= 1 - 2 {sin}^{2} α {cos}^{2} α + 2 {cos}^{2} α {sin}^{2} α$

$= 1$

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Similar questions

Q. The expression

3 [{sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π - α)]

is equal to

3 $[s i n^{4} (\frac{3 π}{2} - α) + s i n^{4} (3 π + α)]$ - $[s i n^{6} (\frac{π}{2} + α) + s i n^{6} (5 π - α)]$ =

Q. The expression,

3 [{sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π - α)]

when simplified is equal to

Q. The value of

3 [{sin}^{4} (\frac{3 π}{2} - x) + {sin}^{4} (3 π + x)] - 2 [{sin}^{6} (\frac{π}{2} + x) + {sin}^{6} (5 π - x)]

for all permissibly value of x , is

Q. If

f (x) = 3 [{sin}^{4} (\frac{3 π}{2} - x) + {sin}^{4} (3 π + x)] - 2 [{sin}^{6} (\frac{π}{2} - x) + {sin}^{6} (5 π - x)]

, then for all permissible values of

x, f (x)

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The expression 3[sin4(3π2−α)+sin4(3π+α)]−2[sin6(π2+α)+sin6(5π+α)] is equal to

The expression $3 [{sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π + α)]$ is equal to