Q2) If cosec theeta - sin theeta = a^3 and sec theeta - cos theeta = b^3, then (a^2 b^2)(a^2 + b^2) =
a) 1 b) -1 c) 2 d) none of these
I have some questions and doubts in Trigonometry. I hope somebody can solve these questions.
Q1) If cosec theeta - cot theeta = 1/2, o< theeta< pie/2, then cos theeta is equal to
a) 5/3 b) 3/5 c) -3/5 d) -5/3
I will post the following questions soon.
P.S. I would also like to have the steps to solve the problem please.
I assume xosec means cosec. If I could have a pie every time I wrote a pi, I would be rich!
To solve this equation exactly, express cosec and cot through sin and cos, add the two fractions in the left-hand side and express as . In general, , but since , both and are positive. You'll get a quadratic equation in .
With these answer options, it is easy to eliminate three of them. As I said, must be positive for in this range, and cannot exceed 1.
It isn't really necessary to solve any equation here.
a)5/3, c) -3/5, and d) -5/3 are obviously impossible (do you see why?) so b) 3/5 is the only possible answer.
If you want to check, cosec= 5/4 and cot= 3/4. Their difference is 5/4- 3/4= 2/4= 1/2.
Did you even try this? It's pretty close to being trivial.I will post the following questions soon.
P.S. I would also like to have the steps to solve the problem please.