Question

cos 60°- cot 45°+ cosec 30°/sec 60°+ tan45°-sin30°

Answer 1

Answer:

$\frac{cos 60^0- cot 45^0+ cosec 30^0}{sec 60^0+ tan45^0-sin30^0}$ = $\frac{3}{5}$

Step-by-step explanation:

To find,

$\frac{cos 60^0- cot 45^0+ cosec 30^0}{sec 60^0+ tan45^0-sin30^0}$

Solution:

cost 60° = $\frac{1}{2}$

cot 45°  = 1

cosec 30°  = 2

sec 60°  = 2

tan 45°  = 1

sine 30°  =  $\frac{1}{2}$

Substituting these values in the given expression we get

$\frac{cos 60^0- cot 45^0+ cosec 30^0}{sec 60^0+ tan45^0-sin30^0}$ = $\frac{\frac{1}{2}-1+2 }{2+1-\frac{1}{2}}$

= $\frac{-\frac{1}{2}+2 }{3-\frac{1}{2}}$

= $\frac{\frac{3}{2} }{\frac{5}{2} }$

= $\frac{3}{5}$

∴ $\frac{cos 60^0- cot 45^0+ cosec 30^0}{sec 60^0+ tan45^0-sin30^0}$ = $\frac{3}{5}$

#SPJ3

Answer 2

ANSWER

$cos 60 - cot45 + cosec 30 \: / \: sec 60+ tan 45 - sin30 \:$

$= 3/5$

EXPLANATION-

Whenever we are given trignometric angle values like 30° 45° 60° we simply put their values.

Values

• $Cos 30= √3/2 \: \: \: Cos 60=1/2 \: \: \: Cos 45=1/√2$
• $Sin30=1/2 \: \: \: Sin 45 =1/√2 \: \: \: Sin 60=√3/2$
• $Tan 30= 1/√3 \: \: \: Tan 45= 1 \: \: \: Tan60= √3$

We can find other needed values through the above-

• Cot is the reciprocal of Tan
• Cosec is the reciprocal of Sin
• Sec is the reciprocal of Cos

So

• $cot 45 = 1/Tan 45 = 1$
• $Sec 60 = 1/Cos60 = 1÷1/2 = 2$$Cosec30 = 1/Sin30= 1÷1/2= 2$

Now putting these values in the question:-

$cos 60 - cot45 + cosec 30 \: / \: sec 60+ tan 45 - sin30 \:$

$= 1/2- 1+2÷2+1-1/2$

$= 3/2÷ 5/2$

$=3/5$

By solving the trignometry functions we will get 3/5

Some Basic important formulas related to Trignomertry are:

$Cos @ = Base / Hypotenuse$

$Sin @ = Perpendicular / Hypotenuse$

$Tan @ = Perpendicular / Base$

As we have learnt earlier that Sec Cosec and Cot are their respective reciprocals so

$Sec @= Hypotenuse / Base$

$Cosec @= Hypotenuse / Perpendicular$

$Cot @ = Base/ Perpendicular$

Trignometry deals with the relationship between side lengths and angles of a triangle.

- Trignometry functions use- They are used to obtain unknown angles and distances from known angles.

Further links -

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/9723562&ved=2ahUKEwjQsNna9tz5AhWg4DgGHT6AACQQjjh6BAgHEAE&usg=AOvVaw0aIZthZCNs8z-QU-neMJEk

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/42063011&ved=2ahUKEwjQsNna9tz5AhWg4DgGHT6AACQQjjh6BAgoEAE&usg=AOvVaw2klrINZRIz67QVNnwGN0pP

CODE# SPJ3