Question

in a ∆ABC, angleA=angleC, is cosA=cosB?​

Answer 1

Answer:

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Given: In triangle ABC

Angle B=90 degree

Angle A=Angle C

To find:

(1) SinA Cos C+Cos ASin C

(2) SinASin B+CosA Cos B

Solution:

In triangle ABC

\angle A+\angle B+\angle C=180^{\circ}∠A+∠B+∠C=180

∘

Using triangle angles sum property

Substitute the values

\angle A+90+\angle A=180∠A+90+∠A=180

2\angle A=180-90=902∠A=180−90=90

$\angle A=\frac{90}{2}=45^{\circ}∠A= 290 =45 ∘$

$\angle A=\angle C=45^{\circ}∠A=∠C=45 ∘$

(1)

Sin 45Cos 45+Cos 45Sin 45Sin45Cos45+Cos45Sin45

$\frac{1}{\sqrt 2}\times \frac{1}{\sqrt 2}+\frac{1}{\sqrt 2}\times \frac{1}{\sqrt 2}$

2 1 × 21 + 21× 21

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

21 + 21 = 21+1 = 22=1=1(2)

Sin 45Sin90+Cos45Cos 90Sin45Sin90+Cos45Cos90

$\frac{1}{\sqrt 2}\times 1+\frac{1}{\sqrt 2}$\times 0 2 1 ×1+ 21 ×0$\frac{1}{\sqrt 2}$ 21

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