Question

lf CosA = 3/4 then find TanA​

Answer 1

Answer:

$\cos(a) = \frac{3}{4} \\ to \: find = \tan(a)$

• we can solve this in 2 ways
• way 01 - identities
• way-02 - formula

WAY 01:-

By identities it is not possible as cos a and tan a are not coming in the same identity

WAY 01:-

$\cos(a) = \frac{adj}{hyp}$

$but \cos(a ) = \frac{3}{4}$

therefore let x be the common multiple,

$adjacent \: side = 3x$

$hyotenuse = 4x$

therefore by applying Pythagoras theorem,

$3 {x}^{2} + {y}^{2} = 4 {x}^{2}$

here y is the 3rd side of triangle

${y}^{2} = 4 {x}^{2} - 3 {x}^{2}$

${y}^{2} = {x}^{2}$

$y = 1x$

Now,

we have,

adjacent side-3x

hypotenuse-4x

oppesite side-1x

therefore,

$\tan(a) = \frac{opposite}{adjacent}$

i.e.

$\tan(a) = \frac{1x}{3x}$

Therefore,

$\tan(a) = \frac{1}{3}$

THERE IS YOUR ANSWER

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