EXERCISE 8.2
1. Evaluate the following:
y sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan’ 45° + cos2 30° - sin60°
cos 45º
sec 30° + cosec 30°
(IV)
sin 30° + tan 45º - cosec 60°
sec 30° + cos 60° + cot 45°
oleh
cos 60° + 4 sec? 30° - tan? 45°
sin 30° + cos2 30°
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Answer:
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BrainlyHelper
Secondary School Math 15+8 pts
Question 1 Evaluate the following
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan^2 45° + cos^2 30° − sin^2 60°
(iii) cos45 / (sec30 + cosec30)
(iv) (sin 30 + tan 45 - cosec 60) / (sec 30 + cos 60 + cot 45)
(v) (5cos^2 60 + 4sec^2 30 - tan^2 45) / (sin^2 30 + cos^2 30)
Class 10 - Math - Introduction to Trigonometry Page 187
by BrainlyHelper 27.07.2017
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abhi178
Abhi178★ Brainly Teacher ★
(1) sin60.cos30 + sin30.cos60
use, formula,
sin( A + B) = sinA.cosB + cosA. sinB
hence,
sin60.cos30 + sin30.cos60 = sin(30+60)
= sin90 = 1
(2) 2tan^2 45° + cos^2 30° − sin^2 60°
= 2 (1)² + (√3/2)² - (√3/2)²
= 2
(3) cos45 / (sec30 + cosec30)
= 1/√2/(2/√3 + 2 )
= √3/2√2( 1 + √3)
= √6(√3 - 1)/8
(4) (sin 30 + tan 45 - cosec 60) / (sec 30 + cos 60 + cot 45)
= (1/2 + 1 - 2/√3)/( 2/√3 + 1/2 + 1)
= (3/2 - 2/√3)/( 2/√3 + 3/2)
=(3√3 - 4)/(4 + 3√3)
(v) (5cos^2 60 + 4sec^2 30 - tan^2 45) / (sin^2 30 + cos^2 30)
= ( 5 ×1/4 + 4 × 4/3 - 1)/( 1/4 + 3/4)
= ( 5/4 + 13/3 )
= 67/12
Answer:
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