Trigonometry Questions for Competitive Exams Part 10th

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.

Q15. Find the value of  tan4⁰ . tan43⁰ . tan47⁰ . tan86⁰ = ?

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

Sol.  Given :-  tan4⁰ . tan43⁰ . tan47⁰ . tan86⁰

Rearranging the given sequence to apply the Quadrant rule

= tan4⁰ . tan86⁰ . tan43⁰ . tan47⁰

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

= tan4⁰ . tan(90⁰ ─ 4⁰) . tan43⁰ . tan(90⁰ ─ 43⁰)

We know that tan (90⁰ - θ) = Cotθ therefore,

= (tan4⁰ . Cot 4⁰) . (tan43⁰ . Cot 43⁰)

We know that tanθ . Cotθ = 1, therefore,

= (1) . (1)

= 1.

Hence the required answer is 1.

Q16. Sin(50⁰ + θ) ─ Cos(40 ─ θ) = ?

Sol. Given :-  Sin(50⁰ + θ) ─ Cos(40 ─ θ)

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

= Sin[90⁰ ─ (40⁰ ─  θ)] ─ Cos(40 ─ θ)

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

= Cos (40⁰ ─  θ) ─ Cos(40 ─ θ)

= 0.

Hence the required answer is 0.

Q17. Find the value of tan405⁰.

Sol. Given :-  tan405⁰.

Applying the quadrant rule we get,

= tan(360⁰ + 45⁰)               {this will lie in the 1^st Quadrant}

We know that tan (360⁰ + θ) = tanθ therefore,

= tan45⁰

= 1.

Hence the required answer is 1.

Q18. Find the value of Sin225⁰.

Sol. Given :-  Sin225⁰.

Applying the quadrant rule we get,

= Sin(180⁰ + 45⁰)               {this will lie in the 3^rd  Quadrant}

We know that Sin (180⁰ + θ) = ─ Sinθ therefore,

= ─ Sin45⁰

= (─1/√2).

Hence the required answer is (─1/√2).

 (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........................