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trigonometric ratios and identities 


 

3. The value of the expression tan 1° tan 2° tan 3° ... tan 89° is
a) 1       b) -1       c) 0       d) None of these
Sol: tan 1° tan 2° tan 3° ... tan 89° = tan(90° - 89°) tan(90° - 88°) tan(90° - 87°)... tan 87° tan 88° tan 89°
= cot 89°cot 88°cot87°...tan 87°tan88°tan89°
= (cot 89° tan 89°) (cot 88° tan 88°)
(cot 87° tan 87°) ...(cot 44° tan 44°) tan 45°
= 1 × 1 × 1 ... × 1 × 1 = 1
Ans: a

 

4. The value of the expression 2 (cos4 60° + sin4 30°) − (tan2 60° + cot2 45°) + 3 sec2 30° is

 


 


⇒ sin(A − B) = sin30°
⇒ A − B = 30°   ... (i)
and cos(A + B) = 1/2 ⇒ cos(A + B) = cos 60°
⇒ A + B = 60° ...(ii)
From (i) and (ii), we get A = 45° and B = 15°
Ans: a

 

11. If cos(40° + x) = sin 30°, then value of x is
a) 19°            b) 20°           c) 21°            d) 22°
Sol: cos(40° + x) = sin 30°
⇒ cos(40° + x) = sin(90° - 60°)
⇒ cos(40° + x) = cos 60°
⇒ 40° + x = 60°
⇒ x = 20°
Ans: b

 

12. Find the value of cot4 A + cot2 A.
a) sin2A - cos2A           b) cot4A - tan4A
c) cosec4A - cosec2A    d) sec4A - sec2A
Sol: cot4 A + cot2 A = (cot2 A)2 + cot2 A
= [cosec2A - 1]2 + (cosec2A - 1)
(1 + cot2 A = cosec2A)
= cosec2A - 2 cosec2A + 1 + cosec2A - 1 = cosec4A - cosec2A
Ans: c

 

13. The value of 2 sin 3A sin A is
a) cos 2A - cos 4A         b) cos 4A - sin 3A
c) cos 7A - cos 4A         d) cos 4A - sin 2A
Sol: Using 2 sinα sinβ = cos(α - β) - cos(α + β),
we get 2 sin 3A sin A = cos(3A - A) - cos(3A + A)
= cos 2A - cos 4A
Ans: a 

 



Posted Date : 05-05-2021

 

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