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Mathematics
Trigonometric ratios
Write the Maximum and Minimum values of \[\cos (\cos x)\].
Mathematics
Trigonometric ratios
The maximum value of the expression $ \dfrac{1}{{{\sin }^{2}}\theta +3\sin \theta \cos \theta +5{{\cos }^{2}}\theta } $ is
A. 0
B. 1
C. 2
D. 3
E. 4
Mathematics
Trigonometric ratios
When using right angle triangle trigonometry , the ratio of adjacent side/hypotenuse is named what?

Mathematics
Trigonometric ratios
A circus artist is climbing a $60m$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30^ \circ }$.
Mathematics
Trigonometric ratios
Prove that: $\sin 780{}^\circ \sin 480{}^\circ +\cos 120{}^\circ \sin 150{}^\circ =\dfrac{1}{2}$.
Mathematics
Trigonometric ratios
Prove that:-
\[\tan {{720}^{\circ }}-\cos {{270}^{\circ }}-\sin {{150}^{\circ }}\cos {{120}^{\circ }}=\dfrac{1}{4}\]
Mathematics
Trigonometric ratios
If $\theta $ lies in the first quadrant and $\cos \theta =\dfrac{8}{17}$, the prove that: $\cos \left( \dfrac{\pi }{6}+\theta \right)+\cos \left( \dfrac{\pi }{4}-\theta \right)+\cos \left( \dfrac{2\pi }{3}-\theta \right)=\left( \dfrac{\sqrt{3}-1}{2}+\dfrac{1}{\sqrt{2}} \right)\dfrac{23}{17}$
Mathematics
Trigonometric ratios
If \[\tan \left( A+B \right)=x\ and\ \tan \left( A-B \right)=y\], find the values of tan2A and tan2B.
Mathematics
Trigonometric ratios
What is the exact value of $${\tan ^2}45 + {\sec ^2}30$$?
Mathematics
Trigonometric ratios
How do you solve \[\cot x = 2\]?
Mathematics
Trigonometric ratios
Simplify the expression:
$\dfrac{{\sin ({{270}^\circ} + x){{\cos }^3}({{720}^\circ} - x) - \sin ({{270}^\circ} - x){{\sin }^3}({{540}^\circ} + x)}}{{\sin ({{90}^\circ} + x)\sin ( - x) - {{\cos }^2}({{180}^\circ} - x)}} + \dfrac{{\cot ({{270}^\circ} - x)}}{{\cos e{c^2}({{450}^\circ} + x)}}$

Mathematics
Trigonometric ratios
Which trigonometric function does not use the hypotenuse in its ratio?
(a) sine
(b) cosine
(c) tangent
(d) secant
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