JEE Main 20268 Apr, Evening shiftMathematicsEasySequence and Series179× since 2002Let α=3+4+8+9+13+14+…\alpha=3+4+8+9+13+14+\ldotsα=3+4+8+9+13+14+… upto 40 terms. If (tanβ)α1020(\tan\beta)^{\frac{\alpha}{1020}}(tanβ)1020α is a root of the equation x2+x−2=0x^2+x-2=0x2+x−2=0, β∈(0,π2)\beta\in\left(0,\frac{\pi}{2}\right)β∈(0,2π), then sin2β+3cos2β\sin^2\beta+3\cos^2\betasin2β+3cos2β is equal to :AOption A. 2BOption B. 74\frac{7}{4}47COption C. 52\frac{5}{2}25DOption D. 32\frac{3}{2}23CheckSkip · show solution
