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If tanθ=27 \tan \theta = \frac{ 2}{7} tanθ=72, what is the value of
cosθ+3sinθcosθ−3sinθ? \frac{ \cos \theta + 3 \sin \theta } { \cos \theta - 3 \sin \theta}? cosθ−3sinθcosθ+3sinθ?
Details and assumptions
You may read up on Trigonometric Functions.
Given that sinθ+cosθ=109\sin \theta + \cos \theta = \frac{10}{9}sinθ+cosθ=910 and sin(2θ)=ab\sin (2\theta) = \frac{a}{b}sin(2θ)=ba, where aaa and bbb are coprime positive integers, what is the value of a+ba + ba+b?
If
∑i=090cos2i∘=ab, \sum_{i=0} ^ {90} \cos ^2 i ^ \circ = \frac {a}{b}, i=0∑90cos2i∘=ba,
where aaa and bbb are positive coprime integers what is the value of a+ba+ba+b?
PPP is a point on a semicircle with diameter AB‾=10\overline{AB}=10AB=10. What is the maximum value of 3AP‾+4BP‾?3\overline{AP}+4\overline{BP}?3AP+4BP?
What is the value of:
(1−1cos72∘)(1+1sin18∘)(1−1sin72∘)(1+1cos18∘)? \left(1-\frac{1}{\cos 72 ^\circ}\right)\left(1+\frac{1}{\sin 18 ^\circ}\right)\left(1-\frac{1}{\sin 72 ^\circ}\right)\left(1+\frac{1}{\cos 18 ^\circ}\right)? (1−cos72∘1)(1+sin18∘1)(1−sin72∘1)(1+cos18∘1)?
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