<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csin%28x%29%20%20%2B%20%20%5Ctan%28x%29%20%7D%7B1%20%2B%20%20%5Csec%28x%29%2

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2 years ago

0%7D%20%20%3D%20%20%5Csin%28x%29%20" id="TexFormula1" title=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " alt=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " align="absmiddle" class="latex-formula">
how do I verify this problem?

Mathematics

1 answer:

GrogVix [38]2 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Simplify the numerator/denominator using the trigonometric identities

• tanx = $\frac{sinx}{cosx}$ and secx = $\frac{1}{cosx}$

sinx + tanx = sinx + $\frac{sinx}{cosx}$ = $\frac{xsinxcosx+sinx}{cosx}$

= $\frac{sinx(1+cosx)}{cosx}$ ← numerator

and

1 + secx = 1 + $\frac{1}{cosx}$ = $\frac{cosx+1}{cosx}$ ← denominator

Putting this together gives

$\frac{sinx(1+cosx)}{cosx}$ × $\frac{cosx}{1+cosx}$

Cancel cosx and (1 + cosx) on numerator/ denominator, leaving

left side = sinx = right side ⇒ verified

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3 years ago

Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge

exis [7]

Answer:

Options A and D are correct choices.

Step-by-step explanation:

We have been given an inequality $x\leq -7$ and we are asked to find the correct options from our given choices.

Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.

(A) $3x\leq -21$

$x\leq \frac{-21}{3}$

$x\leq -7$

We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.

(B) $3x\geq -21$

$x\geq \frac{-21}{3}$

$x\geq -7$

This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.

Dividing inequality by a negative number swaps inequality sign.

$x\geq \frac{21}{-3}$

$x\geq -7$

This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.

(D) $-3x\geq 21$