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fredd [130]
3 years ago
10

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

Mathematics
1 answer:
jek_recluse [69]3 years ago
5 0

\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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Please help. 10 points. Please do not guess. Guesses will be reported.
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3 years ago
HELP!! Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are add
vekshin1
1/4*x -  1/6*y= 5    |*18    
4/5 *x + 3/8*y = 10 | *8

18/4*x                  -3*y= 90
32/5*x                + 3y   = 80
-------------------------
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The answer is a





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