TS EAMCET · Maths · Trigonometric Equations
The number of real roots of the equation \(\sin ^{2020} x-\cos ^{2020} x+2019=2020\) in the interval \(\left(-\frac{3 \pi}{2}, \frac{5 \pi}{2}\right)\)
- A \(1\)
- B \(3\)
- C \(5\)
- D infinitely many
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
Given equation \(\sin ^{2020} x-\cos ^{2020} x+2019=2020\) \(\Rightarrow \quad \sin ^{2020} x=1+\cos ^{2020} x\) the range of LHS is \([0,1]\) and the range of RHS is [1,2] So, for the solution \(\sin ^{2020} x=1\) and \(\cos ^{2020} x=0\) and in the given internal…
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