Question

what is the value of Cot15-Sin15​

Answer 1

Answer:

cos(15)−sin(15)=a  

Squaring both sides :

(cos(15)−sin(15))2=a2

cos2(15)−2cos(15)sin(15)+sin2(15)=a2

1−2cos(15)sin(15)=a2

We know that

2cos(x)sin(x)=sin(2x)

So,

1−sin(30)=a2

1−12=12=a2

a=±12−−√=±1–√2–√

a=±12–√=±2–√2

For angles α such that 0≤α≤90, we have

cos(α)>sin(α) , if 0≤α<45

cos(α)=sin(α) , if α=45

cos(α)<sin(α) , if 45<α≤90

So, we have

cos(15)>sin(15)

cos(15)−sin(15)>0

a>0

So, the valid answer is

a=2–√2

cos(15)−sin(15)=2–√2

Step-by-step explanation: