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3 years ago

What’s answer 1 and 2?

Mathematics

1 answer:

emmasim [6.3K]3 years ago

4 0

hey sorry I need a free point !

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3 years ago

Help 10 points and explain how you get the answer.

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4 years ago

A word that describes how two words relate to each other in a sentence is

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2 years ago

Read 2 more answers

(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

5 0

3 years ago

If 2y=x³ + 2x², find dy/dx when x=2.

scZoUnD [109]

Answer:

Step-by-step explanation:

$\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}$

<u>Given equation</u>:

$2y=x^3+2x^2$

Isolate y by dividing both sides by 2:

$\implies y=\dfrac{1}{2}x^3+x^2$

Differentiate with respect to x:

$\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}$

$\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x$

Finally, substitute x = 2 into the differentiated equation:

$\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}$

Learn more about differentiation here:

brainly.com/question/27958412

brainly.com/question/26488862

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2 years ago