Question

If 29sintheta=21 then find tantheta

Answer 1

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Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{=>tan \ theta=\frac{21}{20}}$

$\bold\orange{Given:}$

$\bold{=>29sin \ theta=21}$

$\bold\pink{To \ find:}$

$\bold{=>tan \ theta}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{=>29sin \ theta=21}$

$\bold{=>sin \ theta=\frac{21}{29}}$

________________________________

$\bold{sin^{2}theta+cos^{2}theta=1}$

$\bold{... Trigonometric \ identity}$

$\bold{=>cos^{2}theta=1-(\frac{21}{29})^{2}}$

$\bold{=>cos^{2}theta=1-\frac{441}{841}}$

$\bold{=>cos^{2}theta=\frac{841-441}{841}}$

$\bold{=>cos^{2}theta=\frac{400}{441}}$

$\bold{On \ taking \ square \ root \ of \ both \ sides}$

$\bold{=>cos \ theta=\frac{20}{21}}$

_________________________________

$\bold{tan \ theta=\frac{sin \ theat}{cos \ theta}}$

$\bold{... Trigonometric \ identity}$

$\bold{=>tan \ theta=\frac{\frac{21}{29}}{\frac{20}{29}}}$

$\bold{=>tan \ theta=\frac{21}{29}×\frac{29}{20}}$

$\bold\purple{\tt{\therefore{=>tan \ theta=\frac{21}{20}}}}$