Math, asked by himanshupandey186, 2 months ago

IF TAN (a+b)=√3 and sin B = ½. find A&B.

Answers

Answered by shrishti0864
2

Answer:

B=15°

Step-by-step explanation:

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Answered by Anonymous
2

 \large \boxed{   \underline{\blue{\sf{given: }}}}

 \sf{tan(a + b) =  \sqrt{3} } \\  \sf{sinb =  \frac{1}{2} }

 \green{  \underline{\sf{we \: know : }}} \\  \sf{tan60 \degree =  \sqrt{3} } \\  \sf{sin30 \degree =  \frac{1}{2} }

 \large \boxed{  \underline{ \sf{solution : }}}

 \sf{tan(a + b) =  \sqrt[]{3}  } \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  ...(1) \\ \sf{tan60 \degree =  \sqrt{3}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: ....(2)}

 \sf{by \: eq(1) \: and \: eq(2)} \\  \sf{tan(a + b) = tan60 \degree} \\   \sf{a + b = 60 \degree \:  \:  \:  \:  \:  \:  \:  \: ...(3)}

 \sf{sinb =  \frac{1}{2} \:  \:  \:  \:  \:  \:  \: \:  \:  \: \:  \:   ...(4) } \\  \sf{sin30 \degree =  \frac{1}{2}  \:  \:  \:  \:  \:  \:  \:  \:  \: ...(5)} \\  \sf{by \: eq(4) \: and \: eq(5)} \\  \sf{sinb = sin30 \degree} \\  \boxed{\sf{b = 30 \degree }}

 \sf{put \: the \: value \: of \: b \: in \: eq(3)} \\  \sf{a + b = 60 \degree} \\  \sf{a + 30 \degree = 60 \degree} \\  \sf{a = 60 \degree  - 30 \degree} \\ \boxed{  \sf{a = 30 \degree}}

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