If a -sin 43 -2-sin 43 - and b -sin 6-2-sin 65 - then the value of 3 a -2 b isA- 0B- 1C- 2D- 3

The correct option is B 1a = sin^4 ( 3π2 α )+sin^4(3π+α) ⇒ a=cos^4 α+sin^4α ⇒ a = 1 2sin^2αcos^2α b =sin^6 ( π2+α )+sin^6(5π α) ⇒ b = cos ^6α+sin^6α ⇒ b =1 3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

If a =sin 43 ...

Question

If $a = {sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)$ and $b = {sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π - α)$ , then the value of $3 a - 2 b$ is

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1$
$a = {sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α) \Rightarrow a = {cos}^{4} α + {sin}^{4} α \Rightarrow a = 1 - 2 {sin}^{2} α {cos}^{2} α b = {sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π - α) \Rightarrow b = {cos}^{6} α + {sin}^{6} α \Rightarrow b = 1 - 3 {sin}^{2} α {cos}^{2} α$

Now,
$3 a - 2 b = 3 - 6 {sin}^{2} α {cos}^{2} α - 2 + 6 {sin}^{2} α {cos}^{2} α = 1$

Suggest Corrections

Similar questions

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)] =

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)]

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

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. 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)

Join BYJU'S Learning Program

Explore more

Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

Join BYJU'S Learning Program

If a=sin4(3π2−α)+sin4(3π+α) and b=sin6(π2+α)+sin6(5π−α), then the value of 3a−2b is

The correct option is B 1a=sin4(3π2−α)+sin4(3π+α)⇒a=cos4α+sin4α⇒a=1−2sin2αcos2αb=sin6(π2+α)+sin6(5π−α)⇒b=cos6α+sin6α⇒b=1−3sin2αcos2α Now, 3a−2b=3−6sin2αcos2α−2+6sin2αcos2α=1

If $a = {sin}^{4} (\frac{3 π}{2} - α) + {sin}^{4} (3 π + α)$ and $b = {sin}^{6} (\frac{π}{2} + α) + {sin}^{6} (5 π - α)$ , then the value of $3 a - 2 b$ is