Question

If 2 sinA = 1 = 2 cosB and <A<t,
* < B < 27, then find the value of
tan A+tan B
COS A-cos B​

Answer 1

Step-by-step explanation:

$2sinA = 1 = 2cosB \\ \implies \: 2sinA = 1 \\ \implies \: sinA = \frac{1}{2} \\ \implies \: sinA = sin30 \degree \\ \implies \: A = 30 \degree \\\\ 1 = 2cosB \\ \implies \: 2cosB = 1 \\ \implies \: cosB = \frac{1}{2} \\ \implies \: cosB = cos60 \degree \\ \implies B = 60 \degree \\ now \\ tanA \: + tanB \\ = tan30 \degree \: + tan60 \degree \\ = \frac{1}{ \sqrt{3} } + \sqrt{3} \\ = \frac{1 + 3}{ \sqrt{3} } \\ \fbox{ \therefore \: tanA \: + tanB = \frac{4}{ \sqrt{3} } }\\ cosA \: - cosB \\ = cos30 \degree \: - cos60 \degree \\ = \frac{ \sqrt{3} }{2} - \frac{1}{2} \\ \fbox{\therefore \: cosA \: - cosB = \frac{ \sqrt{3} - 1 }{2} } \:$