Question

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

Answer 1

Answer:

B=15°

Step-by-step explanation:

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Answer 2

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

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

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

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

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

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

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

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