If tan A - B -3 and sin A - B -1-2 Where A and B are acute angles-Then- Cos2A - Sin2B - -

Tan (A+B)=√(3) And we know that tan 60^∘ =√(3) So, A+B =60^∘………………………………………………….(eq. 1) and, sin(A B)=1/2 We know that sin 30^∘=1/2 So, A B=30^∘……………………………………… ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Trigonometric Ratios

If tan A + B ...

Question

If tan(A+B) = $\sqrt{3}$ and sin(A-B) = $\frac{1}{2}$ Where A and B are acute angles.

Then, Cos2A + Sin2B =__

Open in App

Solution

Tan (A+B)= $\sqrt{3}$

And we know that tan $60^{\circ}$ = $\sqrt{3}$

So, A+B = $60^{\circ}$ ………………………………………………….(eq. 1)

and, sin(A-B)= $\frac{1}{2}$

We know that sin $30^{\circ}$ = $\frac{1}{2}$

So, A-B= $30^{\circ}$ ……………………………………………………(eq. 2)

Adding eq.1 and eq.2, we get

2A= $90^{\circ}$

A=45 & B= $15^{\circ}$

Suggest Corrections

Similar questions

Q. If

A

and

B

are acute angles such that

sin A = {sin}^{2} B, 2 {cos}^{2} A = 3 {cos}^{2} B

; then

Q. If tan(A + B) =

\sqrt 3

and tan(A - B) =

\frac{1}{\sqrt{3}} .

Find A and B where A & B are acute angles.

Q. If

sin A = \frac{1}{\sqrt{2}}

and

cot B = 1

, prove that

sin (A + B) = 1

, where

A

and

B

are acute angles.

Q. Assertion :If

{tan}^{2} A = {tan}^{2} B, {cos}^{2} A = {cos}^{2} B {sin}^{2} A = {sin}^{2} B

, then

A = n π \pm B, n ϵ I

Reason:

tan A = tan B

cos A = cos B, sin A = sin B

, then

A = n π \pm B, n ϵ I

If A and B are acute angles such that tan $A = \frac{1}{2}, t a n B = \frac{1}{3}$ and tan $(A + B) = \frac{t a n A + t a n B}{1 - t a n A t a n B}$ ,find A + B

Join BYJU'S Learning Program

If tan(A+B) =√3 and sin(A-B) = 12 Where A and B are acute angles. Then, Cos2A + Sin2B =__

If tan(A+B) = $\sqrt{3}$ and sin(A-B) = $\frac{1}{2}$ Where A and B are acute angles.

Then, Cos2A + Sin2B =__