Question

If sin a = 1/2 and cos b = 1/2, then find a+b ?

Answer 1

QUESTION :

$\sf{If\:sin\:a=\frac{1}{2}\:and\:cos\:b=\frac{1}{2},}$

$\sf{Then\: find\:the\: value\:of\:a+b.}$

SOLUTION :

$\sf{\:\:\:sin\:a=\frac{1}{2}}$

$\sf{We\: know,\:sin30=\frac{1}{2}}$

$\implies\sf{sin\:a=sin\:30}$

$\implies\sf{a\:=\:30}$

$\sf{\:\:\:cos\:b=\frac{1}{2}}$

$\sf{We\: know,\:cos60=\frac{1}{2}}$

$\implies\sf{cos\:b=cos\:60}$

$\implies\sf{b\:=\:60}$

✪ Now find the value of (a+b)✪

$\sf{a+b}$

† Putting a = 30 and b = 60 †

$\sf{=(30+60)}$

$\sf{=90}$

Hence , the value of (a+b) is 90°.

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★MORE INFORMATION :

Some values of trigonometry:-

• sin30° = 1/2
• sin45° = 1/√2
• sin60° = √3/2
• sin90° = 1
• cos30° = √3/2
• cos45° = 1/√2
• cos60° = 1/2
• cos90° = 0
• tan30° = 1/√3
• tan45° = 1
• tan60° = √3

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Answer 2

$\mathtt{\huge\fbox{Solution :)}}$

Given ,

• Sin(α) = 1/2
• Cos(β) = 1/2

Thus ,

$\sf \hookrightarrow Sin(α) = \frac{1}{2} \\ \\ \sf \hookrightarrow </p><p>Sin(α) = Sin(30) \\ \\ \sf \hookrightarrow </p><p>α = 30$

and

$\sf \hookrightarrow Cos(β) = \frac{1}{2} \\ \\ \sf \hookrightarrow</p><p>Cos(β) = Cos(60) \\ \\ \sf \hookrightarrow </p><p>β = 60</p><p>$

Now , we have to find α + β , so

α + β = 30 + 60 i.e 90

Hence , the value of α + β is 90

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