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

The correct option is D Given that secθ = nbsp; 5/4 secθ = nbsp; 1 + tan^2( θ/2)/1 tan^2( θ/2) ⇒ nbsp; 5/4 = nbsp; 1 + tan^2( θ/2)/1 tan ^2 ( θ/2) ...

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Byju's Answer

Standard XI

Mathematics

Sin2a and Cos2a in Terms of Tana

If secθ = 5/4...

Question

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

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$\frac{1}{9}$

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Solution

The correct option is A

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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Similar questions

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

Q. Prove that :

\frac{t a n θ + s e c θ - 1}{t a n θ - s e c θ + 1}

= sec

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\frac{1 + s i n θ}{c o s θ}

Q. If the value of sin θ is

\frac{4}{5}

, then find the value of

\frac{s e c θ}{c o s e c θ}

Q. If

{s i n}^{2} θ + 5 {c o s}^{2} θ = 4,

then find

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and hence prove that

s e c θ + c o s e c θ = 2 + \frac{2}{\sqrt{3}}

Q. If

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and

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then

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If secθ = 54, then tan θ2 =

The correct option is A 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 $\frac{θ}{2}$ =