In the previous post we have discussed about Measures of Central Tendency Definition and In today's session we are going to discuss about simplifying trig expressions. Trigonometry is deals with the branch of mathematics which is used to compare with the angles and sides of triangles. There are different types of expression and also there are different types of method to simplifying trig expressions. Here we need to follow some steps to solve the trigonometric expression.
Step 1: To solve the trigonometric expression first of all we have to take a trigonometry expression. Suppose we have a trigonometry expression as:
Sec (⊼/ 2 – y) – tan (⊼/ 2 – y) sin (⊼/ 2 – y).
Step 2: Then we use corresponding identities of given trigonometry values. In this expression, in place of Sec (⊼/ 2 – y) we use cosec y, in place of tan (⊼/ 2 – y), we use cot y and in place of sin (⊼/ 2 – y). (know more about simplifying trig expressions, here)
⇨Sec (⊼/ 2 – y) – tan (⊼/ 2 – y) sin (⊼/ 2 – y),
So, using the above values we can write the trigonometry expression as:
= cosec y – cot y cos y, on moving ahead we can also write the expression as:
= cosec y – (cos y / sin y) cos y, (because cot y can also be written as cos y / sin y).
Step 3: Then multiply the value present in the parenthesis to the value present outside the parenthesis. So the above trigonometric expression we can write it as:
= cosec y – (cos y / sin y) cos y, on multiplying we get:
= cosec y – cos 2 y / sin y,
We can also write the cosec y as 1 / sin y, so put this value in place of cosec y.
= 1 / sin y - cos 2 y / sin y, here in this expression sin y is the LCM. So, taking LCM we get the next step of expression as:
= (1 - cos 2 y) / sin y, we can also write the (1 - cos 2 y) as sin 2 y. So, we can write it as:
= sin 2 y / sin y = sin y. This is how we can solve the trigonometric expression. There are different Types of Pollution in the environment. The iit entrance exam is applicable for iit colleges.
Step 1: To solve the trigonometric expression first of all we have to take a trigonometry expression. Suppose we have a trigonometry expression as:
Sec (⊼/ 2 – y) – tan (⊼/ 2 – y) sin (⊼/ 2 – y).
Step 2: Then we use corresponding identities of given trigonometry values. In this expression, in place of Sec (⊼/ 2 – y) we use cosec y, in place of tan (⊼/ 2 – y), we use cot y and in place of sin (⊼/ 2 – y). (know more about simplifying trig expressions, here)
⇨Sec (⊼/ 2 – y) – tan (⊼/ 2 – y) sin (⊼/ 2 – y),
So, using the above values we can write the trigonometry expression as:
= cosec y – cot y cos y, on moving ahead we can also write the expression as:
= cosec y – (cos y / sin y) cos y, (because cot y can also be written as cos y / sin y).
Step 3: Then multiply the value present in the parenthesis to the value present outside the parenthesis. So the above trigonometric expression we can write it as:
= cosec y – (cos y / sin y) cos y, on multiplying we get:
= cosec y – cos 2 y / sin y,
We can also write the cosec y as 1 / sin y, so put this value in place of cosec y.
= 1 / sin y - cos 2 y / sin y, here in this expression sin y is the LCM. So, taking LCM we get the next step of expression as:
= (1 - cos 2 y) / sin y, we can also write the (1 - cos 2 y) as sin 2 y. So, we can write it as:
= sin 2 y / sin y = sin y. This is how we can solve the trigonometric expression. There are different Types of Pollution in the environment. The iit entrance exam is applicable for iit colleges.
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