Answer:
cos B = 
tan B = 
sin B = 
Step-by-step explanation:
In the right triangle, there are three sides and 2 acute angles
- Hypotenuse ⇒ the opposite side of the right angle
- Leg1 and Leg 2 ⇒ the sides of the right angle
The trigonometry functions of one of the acute angles Ф are
- sin Ф = opposite leg/hypotenuse
- cos Ф = adjacent leg/hypotenuse
- tan Ф = opposite leg/adjacent leg
In Δ ACB
∵ ∠C is the right angle
∴ AB is the hypotenuse
∵ AC is the opposite side of ∠B ⇒ leg1
∵ CB is the adjacent side of ∠B ⇒ leg2
→ By using the ratios above
∴ cos B =
, tan B =
, sin B = 
∵ CB = 7, AB = 25, AC = 24
∴ cos B = 
∴ tan B = 
∴ sin B = 
Answer:

Step-by-step explanation:

<span>sinx - cosx =sqrt(2)
Taking square on both sides:
</span>(sinx - cosx)^2 =sqrt(2)^2<span>
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
</span><span>sin^2(x)+cos^2(x) = 1
</span><span>So,
1-2sinxcosx=2
1-1-2sinxcosx=2-1
-</span><span>2sinxcosx = 1
</span><span>Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
</span><span>sin2x = -1</span><span>
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer</span>