Question

tan A = 1/√3 then 7 sin²A + 3cos² A =?
who anwers fast & correctly I will mark as brainliest + Thanks+5.0 vote + i will follow them​​

Answer 1

Answer:

tanA = 1/root

tanA=tan30

A=30

=7sin^2A+3cos^2A

=7(sin30)^2+3(cos30)^2

=7(1/2)^2+3(root3/2)^2

=7×1/4+3×3/4

=7/4+9/4

=16/4

=4 answer

Answer 2

${\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}}$

${\rm{ \tan(A) = \dfrac{1}{ \sqrt{3}}\:then\: 7{ \sin}^{2}(A) + 3{ \cos }^{2} (A) = ?}}$

_________________________________________

${\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}}$

${\red{\rm{7{ \sin}^{2}(A) + 3{ \cos }^{2} (A) = 4}}}$

_________________________________________

${\large{\underline{\pink{\sf{Given:}}}}}$

${\rm{ \tan(A) = \dfrac{1}{ \sqrt{3}}}}$

_________________________________________

${\large{\underline{\blue{To \ Find}}}}$

${\red{\rm{7{ \sin}^{2} (A) + 3{ \cos }^{2} (A) = ?}}}$

_________________________________________

${\purple{\underline{\underline{\red{\boxed{\boxed{\blue{\star{\sf Solution:}}}}}}}}}$

${\rm{We\:are\:Given,}}$

${\rm{ \tan(A) = \dfrac{1}{ \sqrt{3}}}}$

${\therefore{\rm{ A = { \tan}^{-1}( \dfrac{1}{ \sqrt{3}}) }}}$

${\longrightarrow{\rm{ But , \ { \tan}^{-1}( \dfrac{1}{ \sqrt{3}}) = 30 \degree }}}$

${\therefore{\orange{\boxed{\green{ A = 30 \degree}}}}}$

${\rm{ Now,}}$

${\rm{7{ \sin }^{2} (A) + 3{ \cos }^{2} (A) }}$

${\rm{Put\:A= 30 \degree \:in\:above\: equation}}$

${\therefore{\rm{ We\:get,}}}$

${\implies{\rm{7 { \sin}^{2} (30 \degree) + 3 { \cos}^{2} (30 \degree)}}}$

${\rm{but\: {\boxed{\star{ \sin(30 \degree) = \dfrac{1}{2}}}}}}$

${\rm{and\:{\boxed{\star{ \cos(30 \degree) = \dfrac{ \sqrt{3}}{2}}}}}}$

${\implies{\rm{7 { [ \dfrac{1}{2} ]}^{2} + 3{ [ \dfrac{ \sqrt{3}}{2}]}^{2}}}}$

${\implies{\rm{ 7 [ \dfrac{1}{4}]+3 [ \dfrac{ 3}{4}]}}}$

${\implies{\rm{ \dfrac{7}{4}+ [ \dfrac{ 3 \times 3}{4}]}}}$

${\implies{\rm{ \dfrac{7}{4}+ \dfrac{ 9}{4}}}}$

${\implies{\rm{ \dfrac{7 + 9}{4}}}}$

${\implies{\rm{ \dfrac{16}{4}}}}$

${\implies{\rm{ 4 }}}$

${\pink{\therefore{\purple{\boxed{\red{\boxed{\blue{7{ \sin}^{2}(A) + 3{ \cos }^{2} (A) = 4 }}}}}}}}$