Olympiad Maths for Class 11 | Can You Solve This Exponential Trigonometric Equation @mathsmood

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[mathsmood]

Thank you for watching and have a good day 😊

[sy]

Thank you for explaining. I solve by using the relationship between Arithmetic mean and Geometric mean. I introduce the method.
2^x>0, 2^(-x)>0 ∴ [2^x+2^(-x)]/2≧ (2^x)×[2^(-x)] = 1 ∴ 2^x+2^(-x) ≧ 2 (If 2^x = 2^(-x), it is 2^x+2^(-x) = 2 ) By the way, (-2≦) 2cox ≦ 2 .
Therefore 2cosx=2 . ∴ cosx=1 ∴ x=0° (where 0°≦x<360° ) 　　　 ∴ x=2nπ (n: integer)

[tontonbeber]

In the still image it's 2 cosx = 2^x - 2^(-x) but you solve 2 cosx = 2^x + 2^(-x)
With a minus it's much more difficult. I have no idea how to proceed ... except numerically that gives only 1 solution : x = 0.87287555569