Question

<A < ,
1) If 2 sinA = 1 = 12 cosB and
Зл
< B < 21, then find the value of
2
tan A+tan B
cos A-cos B​

Answer 1

Answer:

secret384

12.08.2019

Math

Secondary School

+5 pts

Answered

If 2 sinA=1=√2 cosB and π/2<A<π , 3π/2<B<2π then find value of tanA+tanB/cosA-cosB

2

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Answers

sonuvuce

sonuvuce Ace

Answer:

Given

2sinA = 1

⇒ sinA = 1/2 = sin30°

⇒ A = 30°

Also, √2 cosB = 1

⇒ cosB = 1/√2 = cos45°

⇒ B = 45°

Therefore

\frac{\tan A+\tan B}{\cos A-\cos B}

=\frac{\tan 30^\circ+\tan 45^\circ}{\cos 30^\circ-\cos 45^\circ}

=\frac{(1/\sqrt{3}) +1}{(\sqrt{3}/2)-(1/\sqrt{2})}

=\frac{\sqrt{3}+1}{\sqrt{3}} \times \frac{2}{\sqrt{3}-\sqrt{2}}

=\frac{\sqrt{3}+3}{3} \times \frac{2(\sqrt{3}+\sqrt{2})}{3-2}

=\frac{2}{3}\times (\sqrt{3}+\sqrt{2})(\sqrt{3}+3})

=\frac{2}{3}(\sqrt{3}+\sqrt{2})(\sqrt{3}+3})