Question

If tan (A+B)=root 3 and tan (A-B) =0 ,0 degree A+B <90 degree find sin (A+B) and cos( A-B)​

Answer 1

Step-by-step explanation:

answer and explanation given in picture

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Answer 2

Given:-

๛Tan(A+B)=√3

๛Tan(A-B)=0

$\rule{200}{1}$

To Find:-

➜The Value of Sin(A+B) and Cos(A-B)?

$\rule{200}{1}$

AnsWer:-

☞Cos0°=1

☞Sin60°=$\frac{\sqrt{3}}{2}$

$\rule{200}{1}$

[°•°Tan60°=√3]

↝Tan(A+B)=Tan60

↝A+B=60-(1)

[°•°Tan0°=0]

↝Tan(A-B)=Tan0

↝A-B=0-(2)

✪Add (1)&(2)✪

↝A+B=60

↝A-B=0

★Signs Changed★

↝2A=60

↝B=$\frac{\cancel{60}}{\cancel{2}}$

☞B=30-(3)

✪Using (3) in (2)✪

↝A-30=0

↝A=30-(4)

✪Using (4) and (3) for Sin(A+B)✪

↝Sin(A+B)=Sin(30+30)

☞Sin60°=$\frac{\sqrt{3}}{2}$

✪Using (4) and (3) for Cos(A-B)✪

↝Cos(A-B)=Cos(30-30)

☞Cos0=1

$\rule{200}{2}$