JEE MAIN - Mathematics (2021 - 27th July Evening Shift - No. 16)
If the real part of the complex number $$z = {{3 + 2i\cos \theta } \over {1 - 3i\cos \theta }},\theta \in \left( {0,{\pi \over 2}} \right)$$ is zero, then the value of sin23$$\theta$$ + cos2$$\theta$$ is equal to _______________.
Answer
1
Explanation
Re $$(z) = {{3 - 6{{\cos }^2}\theta } \over {1 + 9{{\cos }^2}\theta }} = 0$$
$$\Rightarrow$$ $$\theta$$ = $${{\pi \over 4}}$$
Hence, sin23$$\theta$$ + cos2$$\theta$$ = 1.
$$\Rightarrow$$ $$\theta$$ = $${{\pi \over 4}}$$
Hence, sin23$$\theta$$ + cos2$$\theta$$ = 1.
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