Question

Sin theta=cos theta then find the value of tan theta +cot theta

Answer 1

$\large{\underline{\bf{\green{Given:-}}}}$

✰ sin∅ = cos∅

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the value of tan∅ +cot∅

$\huge{\underline{\bf{\red{Solution:-}}}}$

$: \implies \rm{\purple{\:tan\theta=\frac{sin\theta}{cos\theta}}}$

$: \implies \rm{\purple{\:cot\theta=\frac{cos\theta}{sin\theta}}}$

$: \implies \rm\:\frac{sin\theta}{cos\theta}+\frac{cos\theta}{sin\theta} \\ \\: \implies \rm\: \frac{ {sin}^{2} \theta + {cos}^{2} \theta }{cos \theta.sin \theta} \\ \\ : \implies \rm\:{ \purple{ {sin}^{2} \theta + {cos}^{2} \theta = 1 }} \\ \\: \implies \rm\: \frac{1}{cos \theta.sin \theta} \\ \\ \rm\:we \: know \:that \: cos \theta = sin \theta \\ \\: \implies \rm\: \frac{1}{cos {}^{2} \theta} \\ \\ : \implies \rm\: {sec}^{2} \theta$

Or

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

$: \implies \rm\: {cosec}^{2} \theta$

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Answer 2

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

$\bold{The \ value \ of \ tan \ theta+cot \ theta}$

$\bold{is \ 2.}$

$\bold\orange{Given:}$

$\bold{=>sin \ theta = \ cos \ theta}$

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

$\bold{=>The \ value \ of \ tan \ theta + \ cot \ theta}$

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

$\bold{Method(I)}$

$\bold{=>sin \ theta=cos \ theta}$

$\bold{we \ know,}$

$\bold{sin \ 45°=\frac{1}{\sqrt2} \ also \ cos \ 45°=\frac{1}{\sqrt2}}$

$\bold{\therefore{theta=45°}}$

$\bold{\therefore{tan45°+cot45°=1+1}}$

$\bold{\therefore{tan45°+cot45°=2}}$

$\bold\purple{\tt{\therefore{tan \ theta + cot \ theta=2}}}$

__________________________________

$\bold{Method(II)}$

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

$\bold{cot=\frac{cos}{sin}}$

$\bold{But, \ sin=cos}$

$\bold{\therefore{tan \ theta=1}}$

$\bold{\therefore{cot \ theta=1}}$

$\bold{\therefore{tan \ theta+cot \ theta=1+1}}$

$\bold{\therefore{tan \ theta+cot \ theta=2}}$

$\bold\purple{\tt{\therefore{The \ value \ of \ tan \ theta + cot \ theta}}}$

$\bold\purple{\tt{is \ 2.}}$