Question

5 sin² thata+3cos² theta =4 find the value of sin 2 thata​

Answer 1

Answer:  1

Step-by-step explanation:

5 sin^2 ∅  +  3 cos^2 ∅  = 4

2 sin^2 ∅  +  3 sin^2 ∅  +  3 cos^2 ∅  =  4

2 sin^2 ∅  +  3(sin^2 ∅ + cos^2 ∅)  =  4

2 sin^2 ∅  +  3   =   4

2 sin^2 ∅  =  1

1 - 2 sin^2 ∅  =  0

cos 2∅  =  0

 2∅  =  pie/2

Therefore,  sin 2∅ = sin (pie/2)

                                = 1 (ANSWER)

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Answer 2

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Given:}}}}$

• $\rm{5\:sin^2\theta+3\:cos^2\theta=4}$

$\large{\underline{\red{\rm{To\: Find:}}}}$

• $\rm{The\: Value\:sin^2\theta=?}$

$\large{\underline{\red{\rm{According\:to\: Question:}}}}$

$\rm{\implies 5\:sin^2\theta+3\:cos^2\theta=4}$

$\rm{\implies 5\:sin^2\theta+3(1-\:sin^2\theta)=4}$

$\rm{\implies 5\:sin^2\theta+3-3\:sin^2\theta=4}$

$\rm{\implies 5\:sin^2\theta-3\:sin^2\theta=4-3}$

$\rm{\implies 2\:sin^2\theta=1}$

$\rm{\implies sin^2\theta=\dfrac{1}{2}}$

Hence,

$\rm{The\: Value\:sin^2\theta=\dfrac{1}{2}}$

Some related formula:-

$\rm{Sin^2\theta+cos^2\theta=1}$

$\rm{Sin^2\theta=1-cos^2\theta}$

$\rm{cos^2\theta=1-sin^2\theta}$