Prove that: (i) cos3A+cosSA+cos7A+cos15A 4cos4A cosSA cos6A (ii) cosA

1.	Prove that: (i) cos3A+cosSA+cos7A+cos15A 4cos4A cosSA cos6A (ii) cosA+cos3A+cos5A+cos7A=4cosA cos2A cos4A (iii) sinA+sin2A+sin4A+sin5A 4cosA2cos3Asin3A (iv) sin3A+sin2A+sinA−4 sinA cosA2cos3A2 (v) cos20∘cos100∘+cos100∘ cos140cos200°=−34 (vi) sinθ2sin7θ2+sin3θ2sin11θ2=sin2θ sin5θ (vii) sinθ2−cos3θ cos=9θ2=sin7θ sin8θ
Answer» Prove that: (i) $c o s 3 A + c o s S A + c o s 7 A + c o s 15 A 4 c o s 4 A c o s S A c o s 6 A$ (ii) $c o s A + c o s 3 A + c o s 5 A + c o s 7 A = 4 c o s A c o s 2 A c o s 4 A$ (iii) $s i n A + s i n 2 A + s i n 4 A + s i n 5 A 4 c o s \frac{A}{2} c o s \frac{3}{A} s i n 3 A$ (iv) $s i n 3 A + s i n 2 A + s i n A - 4 s i n A c o s \frac{A}{2} c o s \frac{3 A}{2}$ (v) $c o s 20^{\circ} c o s 100^{\circ} + c o s 100^{\circ} c o s 140^{c} o s 200 ° = - \frac{3}{4}$ (vi) $s i n \frac{θ}{2} s i n \frac{7 θ}{2} + s i n \frac{3 θ}{2} s i n \frac{11 θ}{2} = s i n 2 θ s i n 5 θ$ (vii) $s i n \frac{θ}{2} - c o s 3 θ c o s = \frac{9 θ}{2} = s i n 7 θ s i n 8 θ$

Prove that: (i) cos3A+cosSA+cos7A+cos15A 4cos4A cosSA cos6A (ii) cosA+cos3A+cos5A+cos7A=4cosA cos2A cos4A (iii) sinA+sin2A+sin4A+sin5A 4cosA2cos3Asin3A (iv) sin3A+sin2A+sinA−4 sinA cosA2cos3A2 (v) cos20∘cos100∘+cos100∘ cos140cos200°=−34 (vi) sinθ2sin7θ2+sin3θ2sin11θ2=sin2θ sin5θ (vii) sinθ2−cos3θ cos=9θ2=sin7θ sin8θ

Answer»

Prove that:
(i) $c o s 3 A + c o s S A + c o s 7 A + c o s 15 A 4 c o s 4 A c o s S A c o s 6 A$
(ii) $c o s A + c o s 3 A + c o s 5 A + c o s 7 A = 4 c o s A c o s 2 A c o s 4 A$
(iii) $s i n A + s i n 2 A + s i n 4 A + s i n 5 A 4 c o s \frac{A}{2} c o s \frac{3}{A} s i n 3 A$
(iv) $s i n 3 A + s i n 2 A + s i n A - 4 s i n A c o s \frac{A}{2} c o s \frac{3 A}{2}$
(v) $c o s 20^{\circ} c o s 100^{\circ} + c o s 100^{\circ} c o s 140^{c} o s 200 ° = - \frac{3}{4}$

(vi) $s i n \frac{θ}{2} s i n \frac{7 θ}{2} + s i n \frac{3 θ}{2} s i n \frac{11 θ}{2} = s i n 2 θ s i n 5 θ$
(vii) $s i n \frac{θ}{2} - c o s 3 θ c o s = \frac{9 θ}{2} = s i n 7 θ s i n 8 θ$

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment