Question

If secA+tanA=4 then cosA=​

Answer 1

$\rm\huge\blue{\underline{\underline{ Question : }}}$

If sec A + tan A = 4, then cos A = ?

$\rm\huge\blue{\underline{\underline{Solution : }}}$

★Given that,

• sec A + tan A = 4

★ To find,

• Value of cos A

★ Let,

• sec A + tan A = 4 ..... (1)

We know the trigonometric identity

• sec² θ + cos² θ = 1

Then, we can write it as,

• (sec θ + tan θ)(sec θ - tan θ) = 1 .

✒ Substitute the value of (1)

$\sf\:\implies 4(\sec\theta - \tan\theta) = 1$

$\sf\:\implies \sec\theta - \tan\theta = \frac{1}{4} ..... (2)$

From the equations (1) & (2). We get,

$\sf\:\implies2 \sec\theta = 1 + \frac{1}{4}$

$\sf\:\implies2 \sec\theta = \frac{4+1}{4}$

$\sf\:\implies \sec\theta = \frac{5}{4} \times \frac{1}{2}$

$\sf\:\implies \sec\theta = \frac{5}{8}$

We know that, cos θ = 1/sec θ

$\sf\:\implies \cos\theta = \frac{1}{\frac{5}{8}}$

$\sf\:\implies \cos\theta = \frac{8}{5}$

$\underline{\boxed{\bf{\purple{ \therefore \cos\theta = \frac{8}{5}}}}}\:\orange{\bigstar}$

★ More Information :

$\boxed{\begin{minipage}{7 cm} Fundamental Trigonometric Identities \\ \\ \sin^{2}\theta + cos^{2}\theta = 1 \\ \\ 1 + tan^{2}\theta = sec^{2}\theta \\ \\1 + cot^{2}\theta=\text{cosec}^2\, \theta \end{minipage}}$

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