# All the Trigonometric identities for the class 10 explained

Learn and know what are the important trigonometric identities for the class 10 students. In trigonometry chapter, after trigonometric ratios, trigonometric identities plays a crucial role. For the students who are in class 10, trigonometric identities are useful in understanding further trigonometry concepts that will come in higher grade. At present, we will know what is trigonometric identity and how many trigonometric identities are there those comes in class 10.

## Meaning of identity in trigonometry:

We know that, in algebra we have identities. For example, a plus b whole square, a square minus b square and so on. Like in algebra, in trigonometry also we have identities. Identity meaning is same in both the cases. For any value of θ, the equation in which trigonometric ratios are involved will be satisfied, which means L.H.S and R.H.S equal we get.

### How many trigonometric identities are there in class 10 syllabus?

Especially, for the class 10 there are 3 main trigonometric identities are there. All these three trigonometric identities are very important to class 10 students.

#### List of trigonometric identities for the class 10:

Important trigonometric identities for class 10 are as follows

The first trigonometric identity is

$\sin ^{ 2 }{ \theta }$ + $\cos ^{ 2 }{ \theta }$ = 1

From the above trigonometric identity we also get,

$\sin ^{ 2 }{ \theta }$ = 1 – $\cos ^{ 2 }{ \theta }$

$\cos ^{ 2 }{ \theta }$ = 1- $\sin ^{ 2 }{ \theta }$

The second trigonometric identity is

$\sec ^{ 2 }{ \theta }$$\tan ^{ 2 }{ \theta }$ = 1

Note:

Here we should not consider  value as odd multiple of 90 degrees.

From the above trigonometric identity we also get,

$\sec ^{ 2 }{ \theta }$ = 1 + $\tan ^{ 2 }{ \theta }$

$\tan ^{ 2 }{ \theta }$ = $\sec ^{ 2 }{ \theta }$ – 1

The third trigonometric identity is

$\cosec ^{ 2 }{ \theta }$$\cot ^{ 2 }{ \theta }$ = 1

Note:

Value we should not take integral multiple of 180 degrees.

From the above trigonometric identity we also get,

$\cosec ^{ 2 }{ \theta }$ = 1 + $\cot ^{ 2 }{ \theta }$

$\cot ^{ 2 }{ \theta }$  = $\cosec ^{ 2 }{ \theta }$ – 1 