Question

If A = 45°, B = 60° then sin A+ cos B =​

Answer 1

Answer:

C=180°-(45°+60°) = 75°

We know that :-

a/sinA=b/sinB=c/sinC

a/sin45°= c/ sin75°

a/c =sin 45°/sin(45°+30°)

a/c =(1/2^1/2)/(sin45°.cos30°+cos45°.sin30°)

a/c =(1/2^1/2)/(1/2^1/2) (3^1/2+ 1)/2

a/c =2/(3^1/2 +1) ×(3^1/2–1)/(3^1/2–1)

a/c =2.(3^1/2–1)/(3–1)

a/c=(3^1/2 - 1 )

a : c = (3^1/2 -1) : 1 . Answer.

Step-by-step explanation:

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Answer 2

Answer:

$\frac{\sqrt{2}+ 1 }{2}$ is the value of sin A + sin B.

Step-by-step explanation:

Explanation:

Given, A = 45° , B = 60°

According to the question we need to find the value of sin A + cos B.

To find the value of sin A + cos B we just need to put the given values of

A = 45° and B = 60° in the  given expression.

Step 1:

From the question we have,

sin A + cos B ..........(i)

On putting the value of A = 45° and B = 60° in (i) we get,

⇒ sin45 + cos 60

As we know that value of sin 45  = $\frac{1}{\sqrt{2} }$ and cos 60 = $\frac{1}{2}$.

⇒ $\frac{1}{\sqrt{2} }$ + $\frac{1}{2}$ = $\frac{\sqrt{2}+ 1 }{2}$.

Final answer:

Hence, the value of sin A + cos B  is equal to $\frac{\sqrt{2}+ 1 }{2}$.

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