Verified Solution • 2025–26 Session moderate

QJEEM25Maa5e7: JEE Main 2025 Mathematics - Class 11 JEEM25Maa5e7 Solution: If , , then is equal to:

If sin⁡x+sin⁡2x=1\sin x + \sin^2 x = 1 , x∈(0,π2)x \in \left(0, \frac{\pi}{2}\right) , then

(cos⁡12x+tan⁡12x)+3(cos⁡10x+cos⁡8x+tan⁡8x)+(cos⁡6x+tan⁡6x)(\cos^{12} x + \tan^{12} x) + 3(\cos^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x) is equal to:

Multiple Choice Options

  • A 3
  • B 4
  • C 2
  • D 1

Step-by-Step Verified Solution

sin⁡x+sin2⁡x=1⇒sin⁡x=cos2⁡x⇒tan⁡x=cos⁡x∴ Given expression =2cos12⁡x+6[cos10⁡x+cos8⁡x]+2cos6⁡x=2[sin6⁡x+3sin5⁡x+3sin4⁡x+sin3⁡x]=2sin3⁡x[(sin⁡x+1)3]=2[sin2⁡x+sin⁡x]3=2

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