SOLUTION: Find all possible solutions: a.) 7cosx = 4 - 2sin^2x b.) 2sec^2x + tan^2x = 3 Thank you.

Question 872773: Find all possible solutions:
a.) 7cosx = 4 - 2sin^2x
b.) 2sec^2x + tan^2x = 3
Thank you.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all possible solutions:
a.) 7cosx = 4 - 2sin^2x
------
7cos(x) = 4 - 2(1-cos^2(x))
7cos(x) = 4 - 2 + 2cos^2(x)
----
2cos^2(x) - 7cos(x) +2 = 0
-----
Use the Quadratic Formula to get:
cos(x) = [7 +- sqrt(49-4*2*2)]/4
cos(x) = [7+-sqrt(33)]/4
cos(x) = 0.3139
x = arccos(0.3139) = +-71.7 degrees
----------------------------------------
b.) 2sec^2x + tan^2x = 3
2(1+tan^2(x)) + tan^2(x) = 3
---------
2 + 3tan^2(x) = 3
tan^2(x) = 1/3
----
tan(x) = 1/sqrt(3)
x = 30 deg or x = 180+30 = 210 degrees
-----------------------------------------
Cheers,
Stan H.
====================

RELATED QUESTIONS
Find all solutions in degress in the interval [0,360] 6cos^2x+7cosx+2=0 Thank you... (answered by Alan3354,ikleyn)

Find all solutions of each equation on the interval 0<=x<=2pie... (answered by Alan3354)

simplify the trigonometric equation. sec^2 - tan^2 (-x) these are my possible... (answered by lynnlo)

2sin^2x+7cosx-5=0 This is as far as I've gotten, not sure how to finalize the answer... (answered by lwsshak3)

Could you please show me how to prove the following identities... A) cos2x=2cos^2x-1 B) (answered by lwsshak3)

find all solutions of the equation in the interval [0,2pi] algebraically 2sin^2x... (answered by jsmallt9)

find all solutions in the interval [0,2pi):... (answered by jsmallt9)

Can you help with solve this: Solve 2sec^2x+tan^2x-3=0 on the interval 0 to... (answered by Alan3354)

Find solutions to 2sin^2x + sinx =... (answered by josgarithmetic)