The value of sin 260° cos 245° + 2 tan 260° - cosec 230° is equal to:
$$\sin^2 60^\circ \cos^2 45^\circ + 2 \tan^2 60^\circ - \csc^2 30^\circ$$
Let's evaluate this using standard trigonometric values:
$\sin 60^\circ = \frac{\sqrt{3}}{2} \implies \sin^2 60^\circ = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4}$
$\cos 45^\circ = \frac{1}{\sqrt{2}} \implies \cos^2 45^\circ = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2}$
$\tan 60^\circ = \sqrt{3} \implies \tan^2 60^\circ = (\sqrt{3})^2 = 3$
$\csc 30^\circ = 2 \implies \csc^2 30^\circ = (2)^2 = 4$
Now, substitute these values back into the expression:
$$\text{Value} = \left(\frac{3}{4} \times \frac{1}{2}\right) + 2(3) - 4$$
$$\text{Value} = \frac{3}{8} + 6 - 4$$
$$\text{Value} = \frac{3}{8} + 2 = \frac{3 + 16}{8} = \mathbf{\frac{19}{8}}$$
Important Questions from Circular Measure of Angles
If sec 4θ = cosec (θ + 20°), then θ is equal to:
Find the value of sin 4 30° + cos 4 30° - sin 25° cos 65° - sin 65° cos25°.
- \(\left( {\frac{{2\tan 30^\circ }}{{1 - {{\tan }^2}\;30^\circ }}} \right){\rm{}} = {\rm{}}?\)
Find the value of cot 25°cot 35°cot 45°cot 55°cot 65°.
The value of
\(\frac{2 \sin^2 30° \tan 60°-3 \cos^2 60° \sec^2 30°}{4\cot^2 45°-\sec^2 60°+ \sin^2 60°+\cos^2 90°}\) is
