Question

if sin theta =cos theta find 3tan^2 theta +2sin^2 theta please answer I will mark it as brainliest....
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Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Given :-

→ sinA = cosA

→ (sinA/cosA) = 1

using formula , (sinA/cosA) = tanA in LHS, Now,

→ tanA = 1

Also , we know that tan45° = 1

Therefore,

→ tanA = tan45°

→ A = 45°

So,

→ 3tan²A + 2sin²A

→ 3tan²45° + 2sin²45°

→ 3(1)² + 2(1/√2)²

→ 3*1 + 2*(1/2)

→ 3 + 1

→ 4 (Ans.)

Answer 2

${ \huge{ \mathfrak{ \underline{ \underline{Question:-}}}}}$

▪ If

${ \bold{ \red{ \sin(theta) = \cos(theta) }}}$

find

${ \bold{ \red{3 { \tan(theta) }^{2} + 2 { \sin(theta) }^{2} }}}$

${ \huge{ \underline{ \underline{ \mathfrak{Solution:-}}}}}$

▪ let theta be equal to alpha (  α ) just for my convenience..

${ \bold { \underline{ \purple{Given-}}}}$

${ \huge{ \bold{ \sin( \alpha ) = \cos( \alpha ) }}}$

▪ Taking cos (  α ) to the L.H.S...

${ \huge{ \bold{ \implies{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \: = 1}}}}$

we know that ,

${ \boxed{ \bold{ \red{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \tan( \alpha ) }}}}$

therefore,

${ \huge{ \bold{ \implies{ \tan( \alpha ) = 1}}}}$

since, the tan value is equal to 1 ...only if the angle is 45°.....

${{ \bold{ \purple{ \tan( \alpha ) = \tan(45) }}}}$

thus,

${ \boxed{ \bold{ \huge{ \implies{ \red{ \alpha = 45 \: \: }}}}}}$

${ \bold{ \underline{ \purple{to \: find}}}}$

${ \bold{3 { \tan( \alpha ) }^{2} + 2 { \sin( \alpha ) }^{2} }}$

substituting the value of   α ....

${ \bold{ = 3 { \tan(45) }^{2} + 2 { \sin(45) }^{2} }}$

${ \boxed{ \bold{ \red{ \tan(45) = 1 \: and \: \sin(45) = \frac{1}{ \sqrt{2} } }}}}$

therefore,

${ \bold {= (3 \times ( {1})^{2}) + (2 \times ( { \frac{1}{ \sqrt{2} } )}^{2} )}}$

${ \bold{ = (3 \times 1) + (2 \times \frac{1}{2}) }}$

${ \bold{ = 3 + 1 = 4}}$

hence,

${ \boxed{ \bold{ \pink{3 { \tan(theta) }^{2} + 2 { \sin(theta) }^{2} = 4}}}}$