Trigonometry Questions for Competitive Exams Part 8th

Following the sequence of last post on basics of Trigonometry I am continuing the basics with their related questions in this post. Let’s prepare this to get full hold on the questions of trigonometry.

Q9. Find the value of  Cot 12⁰ . Cot 38⁰ .  Cot 52⁰ . Cot 60⁰ . Cot 78⁰.

Note:- These types of questions are very easy to solve for the students who learnt or understood the concept of Quadrant rule, identities and formulas

Let’s revise the Quadrant Rule:-

There are total four Quadrant, and the rules regarding these quadrant is known as Quadrant Rule or ASTC Rule.

Rule for 1^st Quadrant:-

Sin (90⁰ - θ) = Cosθ

Cos (90⁰ - θ) = Sinθ

tan (90⁰ - θ) = Cotθ

Cosec (90⁰ - θ) = Secθ

Sec (90⁰ - θ) = Cosecθ

Cot (90⁰ - θ) = tanθ

Sol.  Given :-  Cot 12⁰ . Cot 38⁰ .  Cot 52⁰ . Cot 60⁰ . Cot 78⁰

Applying the quadrant rule of 1^st quadrant we get,

= Cot 12⁰ . Cot 38⁰ . Cot (90⁰ -  38⁰) . Cot 60⁰ . Cot (90⁰ - 12⁰).

We know that Cot (90⁰ - θ) = tanθ therefore,

= Cot 12⁰ . Cot 38⁰ . tan 38⁰ . Cot 60⁰ . tan 12⁰.

= (Cot 12⁰ . tan 12⁰) . (Cot 38⁰ . tan 38⁰) . Cot 60⁰.

But we know that Tanθ × Cotθ = 1

= (1) . (1) . (1/√3).

= (1/√3).

Hence the required answer is (1/√3).

Q10.  Evaluate Sin²20⁰ + Sin²70⁰ – tan²45⁰ .

Sol. Given :-  Sin²20⁰ + Sin²70⁰ – tan²45⁰.

Applying the quadrant rule of 1^st quadrant we get,

= Sin²20⁰ + Sin² (90⁰ – 20⁰) – tan²45⁰.

We know that Sin (90⁰ - θ) = Cosθ therefore,

= (Sin²20⁰ + Cos²20⁰) – tan²45⁰.

We know that Sin²θ + Cos²θ = 1 and tan45⁰ = 1 therefore,

= (1) – (1)²

= 1 -1 = 0.

Hence the required answer = 0.

Q11. Evaluate Cos64⁰. Cos26⁰ – Sin64⁰. Sin26⁰

Sol. Given :-  Cos64⁰. Cos26⁰ – Sin64⁰. Sin26⁰

Applying the quadrant rule of 1^st quadrant we get,

= Cos (90⁰ - 26⁰). Cos26⁰ – Sin (90⁰ - 26⁰). Sin26⁰.

We know that Sin (90⁰ - θ) = Cosθ  and Cos (90⁰ - θ) = Sinθ therefore,

= Sin26⁰. Cos26⁰ – Cos 26⁰. Sin26⁰.

= 0.

Hence the required answer = 0.

(Note you may say that this is so long but dear this is the only way to explain the whole concept of the question to you now its upto you that how fast and short handedly you can solve these type of questions)                                                                        

Hope you have enjoyed the base concept of this chapter till now. More Conceptual enjoyment will be continued for you soon, just keep visiting this blog regularly and writing me your related queries through comment or forum.

Best of Luck for Exams. To be continued soon........................