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RD Chapter 5 Trigonometric Ratios Ex 5.1 Solutions

Question - 11 : - If 3 cot 0 = 2, find the value of  .

Answer - 11 : -


Question - 12 : - If tan θ = a/b, prove that

Answer - 12 : -


Question - 13 : - If sec θ = 13/5, show that 2sinsθ 

Answer - 13 : -

Given,
sec θ = 13/5
We know that,
sec θ = 1/ cos θ
⇒ cos θ = 1/ sec θ = 1/ (13/5)
∴ cos θ = 5/13 ……. (1)
By definition,
cos θ = adjacent side/ hypotenuse ….. (2)
Comparing (1) and (2), we have
Adjacent side = 5 and hypotenuse = 13
By Pythagoras theorem,
Opposite side = √((hypotenuse) 2 – (adjacent side)2)
= √(132 – 52)
= √(169 – 25)
= √(144)
= 12
Thus, opposite side = 12
By definition,
tan θ = opposite side/ adjacent side
∴ tan θ = 12/ 5
 
From, let’s divide the numerator and denominator by cos θ.
We get,
(2 tan θ – 3) / (4 tan θ – 9)
⇒ (2(12/5) – 3) / (4(12/5) – 9) [using the value of tan θ]
⇒ (24 – 15) / (48 – 45) [After taking LCM and cancelling it]
⇒ 9/3 = 3
 
∴ = 3

Question - 14 : - If cos θ 12/13, show that sin θ (1 – tan θ) 

Answer - 14 : -


Question - 15 : -

Answer - 15 : -


Question - 16 : -

Answer - 16 : -


Question - 17 : - If sec θ = 5/4, find the value of  

Answer - 17 : -


Question - 18 : -

Answer - 18 : -


Question - 19 : -

Answer - 19 : -


Question - 20 : -

Answer - 20 : -


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