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3 years ago

Verify the identity. (cos x/ 1+ sin x) + (1+ sin x/cos x) = 2 sec x

Mathematics

1 answer:

Gekata [30.6K]3 years ago

8 0

Answer:

LHS

$\frac{cos x}{1+ sin x} + \frac{1+ sin x}{cos x} \\=\frac{cos2(x)+1+2sin(x)+sin2(x)}{cos(x)(1+sin(x)} \\= \frac{2+2sin(x)}{cos(x)(1+sin(x))} \\\\=\frac{2 (1 + sin(x))}{cos(x)(1+sin(x))} \\= \frac{2}{cos (x)} \\= 2 sec x$

= RHS PROVED

hope it helps :)

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Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

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It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

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Let's identify like terms as below.

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Hope this helps.

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Thank you

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Verify the identity. (cos x/ 1+ sin x) + (1+ sin x/cos x) = 2 sec x​

Verify the identity. (cos x/ 1+ sin x) + (1+ sin x/cos x) = 2 sec x