Question

2. From the following figure, find the values of
(i) cos B
(ii) tan C
(iii) sin'B + cos²B
(iv) sin B.cos C + cos B.sin C
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Answer 1

Question -> from the following figure, find the value of

(i) cosB (ii) tanC (iii) sin²B + cos²B

(iv) sinB cosC + cosB sinC

Solution : from figure it is clear that, ABC is an right angled triangle.

AB = 8, BC = 17 so, CA = √(BC² - AB²)

= √(17² - 8²) = 15

Now cosB = AB/BC = 8/17

tanC = AB/AC = 8/15

sin²B + cos²B = (AC/BC)² + (AB/BC)²

= (15/17)² + (8/17)²

= 225/289 + 64/289

= 289/289 = 1

sinB cosC + cosB sinC = (AC/BC) × (AC/BC) + (AB/BC) × (AB/BC)

= 15/17 × 15/17 + 8/17 × 8/17

= 225/289 + 64/289

= 289/289 = 1

Therefore (i) cosB = 8/17

(ii) tanC = 8/15

(iii) sin²B + cos²B = 1

(iv) sinB cosC + cosB sinC = 1