SOLUTION: If 7^sin²x - 7^cos²x = 8 find the value of x.

Question 1209561: If 7^sin²x - 7^cos²x = 8
find the value of x.

Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.
If 7^sin²x - 7^cos²x = 8
find the value of x.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The starting equation is

        7^(sin^2(x)) - 7^(cos^2(x)) = 8.

Due to OBVIOUS reasons, this equation has no real solutions.

Indeed, sin^2(x) has the maximum value of 1; hence, 7^(sin^2(x)) has maximum value of 7.

Next, from 7^(sin^2(x)), the equation subtracts 7^(cos^2(x)), which is non-negative
real number, so the left side of the equation CAN NOT be greater than 7.

        A fortiori, it can not be 8.

At this point, my solution is complete, and the

ANSWER   is:   this given equation has no solution/solutions in real numbers.

RELATED QUESTIONS
if x is the measure of a positive acute angle and cos x= 7/32 find the value of sin... (answered by jsmallt9)

If sin(x) + cos(x) = 2/3, then find the value of sin(2x). (answered by reviewermath)

7. If tan(x) = 2 and x ∈ [180◦ , 270◦ ]. Determine the value of (i)... (answered by math_helper)

If p = cos x + cos 2x and q = sin x + sin 2x, find the value of... (answered by Alan3354)

if sin x= 4/5, where 0 (answered by edjones)
If sin(x)=-3/5 and cos(x)>0, find the value of... (answered by Alan3354)
sin(x) = 8/17 and π/2 (answered by Alan3354)
if sin A=2.511x, cos A=3.06x and sin 2A=3.939x, find the value of... (answered by lwsshak3)
Suppose sin x = 1/7 cos x > 0, sin y = −2/5 and cos y < 0. Then cos x = cos y (answered by ewatrrr)