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3 years ago

I need the answers for 1-6

Mathematics

1 answer:

andrezito [222]3 years ago

7 0

Answer:

ac and fb , ae and fd , ec and db
sr, tx, st

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jenyasd209 [6]

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2 years ago

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3 years ago

(1+tanx)/(sinx+cosx)=secx

jek_recluse [69]

$\frac{1+\tan x}{\sin x+\cos x}=\sec x$ is proved

<h3><u>Solution:</u></h3>

Given that,

$\frac{1+\tan x}{\sin x+\cos x}=\sec x$ ------- (1)

First we will simplify the LHS and then compare it with RHS

$\text { L. H.S }=\frac{1+\tan x}{\sin x+\cos x}$ ------ (2)

$\text {We know that } \tan x=\frac{\sin x}{\cos x}$

Substitute this in eqn (2)

$=\frac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}$

On simplification we get,

$=\frac{\frac{\sin x+\cos x}{\cos x}}{\sin x+\cos x}$

$=\frac{\sin x+\cos x}{\cos x} \times \frac{1}{\sin x+\cos x}$

Cancelling the common terms (sinx + cosx)

$=\frac{1}{c o s x}$

We know secant is inverse of cosine

$=\sec x=R . H . S$

Thus L.H.S = R.H.S

$\frac{1+\tan x}{\sin x+\cos x}=\sec x$

Hence proved

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3 years ago