Answer: 4
<u>Step-by-step explanation:</u>
3(x) : 8
<u> *2 </u>: <u> *2 </u>
= 24 : 16
⇒ 6x = 24
⇒ x = 4
Answer: 2sin^2x+sin2x+cos2x=0 ..... (1).
By using the trigonometric identities below :
sin2x=2sinxcosx
cos2x=cos^2x-sin^2x
We substitute the trigonometric identities into (1).
2sin^2x+2sinxcosx+cos^2x-sin^2x=0
By combining like terms .
sin^2x+2sinxcosx+cos^2x=0.....(2)
The equation (2) is equivalent to the following expression (3).
(sinx+cosx)(sinx+cosx)=0 .....(3).
sinx+cosx=0
cosx=-sinx
divide both sides by cosx
1=-sinx/cosx
-1=sinx/cosx
sinx/cosx=tanx
substitute
-1=tanx
tanx=-1
tangent is negative in 2nd and 4th quadrants
tan135º=-1 (one answer)
tan315º=-1 (second answer)
Step-by-step explanation:
Please refer to the trigonometric identities used and explained above .
E^2x -2e^x -8=0 => e<span>^(2x) -2e^x -8=0
Temporarily replace e^x with y.
Then (y)^2 - 2y - 8 = 0. Factors are (y-4) and (y+2).
Roots are y = 4 and y= -2.
Now remembering that we temporarily replaced e^x with y, we let
y=4 = e^x. We need to solve for x. Taking the natural log of both sides, we get:
ln 4 = x (answer)
We have to discard the other root (y= -2), because we cannot take the ln of a negative number.
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It is <span>reflection across y = x
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