If sec- - 5-4- then tan -2 -

Given that secθ = 5/4 secθ = 1 + tan^2( θ/2)/1 tan^2( θ/2) ⇒ 5/4 = 1 + tan^2( θ/2)/1 tan ^2 ( θ/2) ⇒ 5 5 tan^2( θ/2) = 4 + 4 tan^2 ( θ/2) ⇒ 9 tan^2 ...

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Byju's Answer

Standard XIII

Mathematics

Sin2A and Cos2A in Terms of tanA

If secθ = 5/4...

Question

If sec $θ$ = $\frac{5}{4}$ , then tan $\frac{θ}{2}$ =

$\frac{1}{3}$

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$\frac{3}{4}$

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$\frac{1}{4}$

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$\frac{1}{9}$

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Solution

The correct option is A
$\frac{1}{3}$

Given that sec $θ$ = $\frac{5}{4}$

sec $θ$ = $\frac{1 + t a n^{2} (\frac{θ}{2})}{1 - t a n^{2} (\frac{θ}{2})}$ $\Rightarrow$ $\frac{5}{4}$ = $\frac{1 + t a n^{2} (\frac{θ}{2})}{1 - t a n^{2} (\frac{θ}{2})}$

$\Rightarrow$ $5 - 5 t a n^{2} (\frac{θ}{2}) = 4 + 4 t a n^{2} (\frac{θ}{2})$

$\Rightarrow$ $9 t a n^{2} (\frac{θ}{2})$ = 1 $\Rightarrow$ $t a n (\frac{θ}{2})$ = $\frac{1}{3}$ .

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If secθ = 54, then tan θ2 =

The correct option is A 13 Given that secθ = 54 secθ = 1+tan2(θ2)1−tan2(θ2) ⇒ 54 = 1+tan2(θ2)1−tan2(θ2) ⇒ 5−5tan2(θ2)=4+4tan2(θ2) ⇒ 9tan2(θ2) = 1 ⇒ tan(θ2) = 13.

If sec $θ$ = $\frac{5}{4}$ , then tan $\frac{θ}{2}$ =