textIf cos α + textcos β = texta text, textsin α + textsin β = textb textand α - β = 2 θ text, textthen ( textcos 3 θ / textcos θ ) is equal to

Question

textIf cos α + textcos β = texta text, textsin α + textsin β = textb textand α - β = 2 θ text, textthen ( textcos 3 θ / textcos θ ) is equal to (A) a2+b2-2 (B) a2+b2-3 (C) 3-a2-b2 (D) (a2 + b2/4)

Tardigrade Admin · Accepted Answer

( cos 3 θ/ cos θ)=4 cos 2 θ-3=2(1+ cos 2 θ)-3 =2 cos 2 θ-1=2 cos (α-β)-1 Now, ( cos 2 α+ sin 2 α)+( cos 2 β+ sin 2 β)+2 cos (α-β)= a 2+ b 2 ⇒ 2 cos (α-β)= a 2+ b 2-2 ⇒ ( cos 3 θ/ cos θ)= a 2+ b 2-3

Q. $If cos α + cos β = a, sin α + sin β = b and α - β = 2 θ, then \frac{cos 3 θ}{cos θ} i se q u a lt o$

$a^{2} + b^{2} - 2$

$a^{2} + b^{2} - 3$

$3 - a^{2} - b^{2}$

$\frac{a ^{2} + b ^{2}}{4}$

Q. If cos α+cos β=a, sin α+sin β=b and α−β=2θ, then cos θcos 3θ​isequalto

a2+b2−2

a2+b2−3

3−a2−b2

4a2+b2​

cosθcos3θ​=4cos2θ−3=2(1+cos2θ)−3 =2cos2θ−1=2cos(α−β)−1 Now, (cos2α+sin2α)+(cos2β+sin2β)+2cos(α−β)=a2+b2 ⇒2cos(α−β)=a2+b2−2 ⇒cosθcos3θ​=a2+b2−3

Q. $If cos α + cos β = a, sin α + sin β = b and α - β = 2 θ, then \frac{cos 3 θ}{cos θ} i se q u a lt o$

$a^{2} + b^{2} - 2$

$a^{2} + b^{2} - 3$

$3 - a^{2} - b^{2}$

$\frac{a ^{2} + b ^{2}}{4}$