Title Trigonometry & Gymnosperm- Daily-8 MCQ (Set-A)-With Solve.pdf ✅

2 6. sin2 (60 + ) + sin2 + sin2 (60 – ) + sin2 30 = z n‡j, z Gi gvb KZ? 3 2 0 1 2 7 4 DËi: 7 4 e ̈vL ̈v: awi,  = 0 Zvn‡j, = sin2 60+ sin + sin2 60 + sin2 30 =    3 2 2 +    3 2 2 +     1 2 2 = 3 4 + 3 4 + 1 4 = 7 4 7. hw`, cos = 1 2     x + 1 x nq, Z‡e cos(20) Gi gvb KZ? 1 2    x 10 + 1 x 10 1 2     x 32 + 1 x 32 1 2    x 20 + 1 x 20 1 2    x 8 + 1 x 8 DËi: 1 2    x 20 + 1 x 20 e ̈vL ̈v: Shortcut: cosn = 1 2    x n + 1 x n ZvB, cos(20) = 1 2    x 20 + 1 x 20 8. sin(4x + 1) Gi ch©vq KZ? 4  2  2 DËi:  2 e ̈vL ̈v: x Gi mnM 4 I sinx dvsk‡bi ch©vq = 2  sin(4x + 1) Gi ch©vqKvj = 2 4 =  2 9. sin21 = p n‡j, sin42 Gi gvb †KvbwU? 2p 2p p 2 – 1 2 1 – p 2 2p 1 – p 2 DËi: 2p 1 – p 2 e ̈vL ̈v: sin42 = sin(2  21 = 2sin21cos21 cos2  = 1 – sin2  = 2p 1 – p 2 10. GKwU wÎfz‡Ri `ywU evû 4 I 8 Ges Zv‡`i AšÍf©y3 †KvY 60 n‡j, wÎfz‡Ri †ÿÎdj KZ eM© GKK? 2 3 3 3 4 8 3 DËi: 8 3 e ̈vL ̈v: †ÿÎdj = 1 2 absin = 1 2  4  8  sin60 = 8 3 eM© GKK 11. ABC wÎfz‡R AB = 3, BC = 4 Ges CA = 5 n‡j, A kxl©we›`y n‡Z BC Gi Dci Aw1⁄4Z j‡¤^i ˆ`N© ̈ KZ GKK? 3 3 9 6 DËi: 3 e ̈vL ̈v: s = 3 + 4 + 5 2 = 6  = 6(6 – 3)(6 – 4)(6 – 5) = 6  3  2  1 = 6 Avevi,  = 1 2  BC  AD  6 = 1 2  4  AD  AD = 6  2 4 = 3 GKK A B C 3 5 D 4 12. cos2A = 1 3 n‡j, sinA = KZ?  1 5  1 3  1 2  2 3 DËi:  1 3 e ̈vL ̈v: cos2A = 1 3  1 – 2sin2A = 1 3  2sin2A = 2 3  sin2A = 2 6  sinA =  1 3 13. wÎfz‡Ri wZbwU evû 5, 6 Ges 7 GKK n‡j, e„nËg †KvY KZ? sin–1     4 11 cos–1     4 11 sin–1     13 14 cos–1     1 5 DËi: cos–1     1 5 e ̈vL ̈v:  5 7 6  cos5 2 + 6 2 – 7 2 2  5  6   = cos–1     1 5