Verified Solution • 2025–26 Session moderate

QJEEM21Ma949c: JEE Main 2021 Mathematics - Class 11 JEEM21Ma949c Solution: If the real part of the complex number is zero, then the value…

If the real part of the complex number z=3+2icos⁡θ1−3icos⁡θ,θ∈(0,π2)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 θ\theta + cos2 θ\theta is equal to _______________.

Step-by-Step Verified Solution

Re (z)=3−6cos⁡2θ1+9cos⁡2θ=0(z) = {{3 - 6{{\cos }^2}\theta } \over {1 + 9{{\cos }^2}\theta }} = 0

⇒\Rightarrow θ\theta = π4{{\pi \over 4}}

Hence, sin23 θ\theta + cos2 θ\theta = 1.

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring