Question

sin alpha + sin beta =1/2 and cos alpha + cos beta=5/4 then tan alpha + tan beta=​

Answer 1

Answer:

11th

Maths

Trigonometric Functions

Trigonometric Functions of Sum and Difference of Two angles

If cosalpha = 12/13 and s...

MATHS

If cosα=

13

12

and sinβ=

5

4

then find sin(α+β).

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ANSWER

If cosα=

13

12

Then, adjacent side of the right angled triangle containing angle α=12 and hypotenuse =15

Using pythagoras theorem, we get the opposite side =5

Now we have, sinα=

Hypotenuse

Opposite

=

13

5

If sinβ=

5

4

Then, opposite side of the right angled triangle containing angle β=4 and hypotenuse =5

Using pythagoras theorem, we get the adjacent side =3

Now we have, cosβ=

Hypotenuse

Adjacent

=

5

3

We know that sin(A+B)=sinAcosB+cosAsinB

sin(α+β)=sinαcosβ+cosαsinβ=

13

5

×

5

3

+

13

12

×

5

4

=

65

15

+

65

48

=

65

63