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How to Do Trigonometric Functions?

TopWhenever we solve Trigonometry problems we have to deal with trigonometric formula. let's learn How to Do Trigonometric Functions? For understating the concept of Trigonometric Functions, you must have the knowledge of all the basic functions of trigonometry so, for solving trigonometric function we need to go through some examples.

Example 1: Solve the equation given as cotx/cosecx + tan x?
For solving this type of equation, we need to convert the trigonometric variable into simplest form. = cotx/cosecx,
We can write cotx as 1/tanx,
= cosecx as 1/sinx, and
= tanx as sinx/cosx,

Put this value in the above equation and we will get:
= (1/tanx )/ (1/sinx) +sinx/cosx,

Now, tanx can be written as sinx/cosx ,on putting this value in the above equation as:
= 1/(sinx/cosx) / (1/sinx) +sinx/cosx

We can rewrite the equation as:
= cosx/sinx *sinx + sinx/cosx,

Now, sinx gets cancel with sinx and we will get the required answer as cosx.+sinx/cosx.
The required simplified equation is (cosx +sinx)/cosx.
In this way, we can simplify any expression.

Example 2: Solve the equation given as: (cotx +tanx ) *cosx ?
Solution: = (cotx +tanx ) *cosx,
= cotx can be written as 1/tanx, so we can rewrite the given equation as:
= (1/tanx +tanx)*cosx,
Now, tanx can be written as sinx /cosx,
= (1/(sinx/cosx) + (sinx /cosx))*cosx,
= (cosx/sinx +sinx/cosx )*cosx,
Now, on taking LCM we will get:
= (cos2x+sin2x/cosx*sinx)*cosx,
Now, we can write sin2x +cos2x=1
So, we can write above equation as:
= (1/cosx*sinx) *cosx,
= (1/cosx *1/sinx)*cosx,
= (secx *cosecx)*cosx,
Now, we can write cosx as 1/secx so, we will rewrite the equation as:
= secx *cosecx *1/secx,
So, secx gets cancel with secx and we will get the solution as:
= cosecx.

Example:
Solve the equation given as: cotx + 1 / cosecx ?
Solution: cotx can be written as 1/tanx,
tanx can be written as sinx/cosx,
cotx can be written as cosx/sinx, and
We can write cosecx as 1/sinx.
Now, putting all these values in the given equation we will get:
= cosx /sinx +1/1/sinx,
We can write this equation as:
= (cosx +sinx ) * sinnx *1/sinx,
So, sinx gets cancel with sinx and we will get:
= cosx + sinx,
So, the required equation can be simplified as cosx + sinx.