Question

if tan theta=20/21,then find the value of other trigonometric ratios (solve using identities)​

Answer 1

Step-by-step explanation:

ANSWER:-

We know that

Tan²0 +1 = Sec²0

Placing value of Tan0 ,

${(\frac{20}{21} )}^{2} + 1 = { \sec }^{2}$

$\frac{400 + 441}{441} = { \sec }^{2}$

$\frac{841}{441} = { \sec }^{2}theta$

$\sec \theta = \frac{29}{21}$

Now we know that:

sec0 = 1/ cos0

cos0 = 21/29

Placing value in

Sin²0+cos²0=1

${ \sin}^{2} \theta = 1 + \frac{441}{841}$

${ \sin}^{2} \theta = \frac{841-441}{841}$

${ \sin}^{2} \theta = \frac{400}{841}$

sin0 = 20/29

Now we know that sin0= 1/cosec0

So,

cosec0= 29/20

And also,

Tan0 = 1/cot0

Cot0 = 21/20

Note:-

0 in all angles refers to theta