How to solve basic problems in trigonometry?(concept-2)

Mathematics tutors give great importance to Trigonometry

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships among the sides and angles of a triangle.Word trigonometry was originated from the Greek word, where, ‘TRI‘ means Three‘GON‘ means sides and the ‘METRON’ means to measure. It’s an ancient and probably most widely used branch Mathematics. For basic learning, I am dividing trigonometry in two part:-

1 Trigonometry based on right triangles

1 Trigonometry based on non-right triangles.

In this post, we will discuss problems based on trigonometric ratios of a few specific angles like 0°,30°, 45°, 60° and 90°. Mathematics tutors use different tricks to form this table. I will discuss my tricks in a separate post

<img src="trigonometric table.jpg" alt="trigonometric table">

Concept-2

In a trigonometric problem, If we are given a trigonometric ratio with a specific angle, we will first put the value of that ratio from above table and do simplification. Simplification is usually based on L.C.M and rationalisation.

Example-1 Find the value of 4/3 tan²60° + 3 cos²30° – 2 sec²30° – 3/4 cot²60°

Solution:  4/3 tan²60° + 3 cos²30° – 2 sec²30° – 3/4 cot²60°

=4/3(√3)²+3(√3/2)²-2(2/√3)²-3/4(1/√3)²
=4/3(3)+3(3/4)-2(4/3)-3/4(1/3)
=4+9/4-8/3-1/3
=4+9/4-3
=16+9-12/3
=13/3

Example-2 If A = 60° and B = 30°, verify sin (A – B) = sin A cos B – cos A sin B

Solution:

L.H.S. = sin (A – B)

= sin (60° – 30°)

= sin 30°

= ½

R.H.S. = sin A cos B – cos A sin B

= sin 60° cos 30° – cos 60° sin 30°

32×3212×12

= ¾ – ¼

= 2/4

= ½

Therefore, L.H.S. = R.H.S. (Proved)

To get a better understanding of the concept you should check all my posts of Mathematics tutors series. you can check them by clicking on the links given below

First post- concept one

Second post- concept two(current post)

Third post -Concept three

Fourth post -Concept four

<img src="demo.png" alt="demo">

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