Question

Cos60°/sin30° + 2cos 0°/sin90°=k/2

Answer 1

Answer:

k=6

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Answer 2

$\sf\huge\blue{\underline{\underline{ Question : }}}$

• $\sf\:\frac{\cos60}{\sin30} + \frac{2\:cos0}{sin90}=\frac{k}{2}$

$\sf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

$\sf\:\frac{\cos60}{\sin30} + \frac{2\:cos0}{sin90}=\frac{k}{2}$

★ To find,

• Value of k.

★ Let,

$\sf\:\implies \frac{\cos60}{\sin30} + \frac{2\:cos0}{sin90}=\frac{k}{2}$

• cos 60° = 1/2
• sin 30° = 1/2
• cos 0° = 1
• sin 90° = 1

$\sf\:\implies \frac{\frac{1}{2}}{\frac{1}{2}} + \frac{2(1)}{1} = \frac{k}{2}$

$\sf\:\implies 1 + 2 = \frac{k}{2}$

$\sf\:\implies 3 = \frac{k}{2}$

$\sf\:\implies k = 3 \times 2$

$\sf\:\implies k = 6$

$\underline{\boxed{\bf{\purple{ \therefore k = 6.}}}}\:\orange{\bigstar}$

★ More information:

$\boxed{\begin{minipage}{8 cm} Fundamental Trigonometric Identities \\ \\ :\implies\sin^{2}\theta + cos^{2}\theta = 1 \\ \\ :\implies 1 + tan^{2}\theta = sec^{2}\theta \\ \\ : \implies 1 + cot^{2}\theta=\text{cosec}^2\, \theta \end{minipage}}$

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