Answers

The Brainliest Answer!
2016-03-31T05:57:33+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Solution


tan θ – cot θ = a ………. (A)


cos θ + sin θ = b ………. (B) 


Squaring both sides of (B) we get, 


cos2 θ + sin2 θ + 2cos θ sin θ = b2


or, 1 + 2 cos θ sin θ = b2


or, 2 cos θ sin θ = b2 - 1 ………. (C) 


Again, from (A) we get, (sin θ/cos θ) – (cos θ/sin θ) = a 


or, (sin2 θ - cos2 θ)/(cos θ sin θ) = a 


or, sin2θ - cos2θ = a sin θ cos θ


or, (sin θ + cos θ) (sin θ - cos θ) = a ∙ (b2 - 1)/2 ………. [by (C)]


or, b(sin θ - cos θ)= (½) a (b2 - 1) [by (B)] 


or, b2 (sin θ - cos θ)2 = (1/4) a2 (b2 - 1)2, [Squaring both the sides] 


or, b2 [(sin θ + cos θ)2 - 4 sinθ cos θ] = (1/4) a2 (b2 - 1)2


or, b2 [b2 - 2 ∙ (b2 - 1)] = (1/4) a2 (b2 - 1)2 [from (B) and (C)] 


or, 4b2 (2 - b2) = a2 (b2 - 1)2


which is the required θ-eliminate.
2 5 2
2016-03-31T06:07:59+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Tan θ – cot θ = a ………. (i)
cos θ + sin θ = b ………. (ii) 

Squaring both sides of (B) we get, 

cos2 θ + sin2 θ + 2cos θ sin θ = b2
= 1 + 2 cos θ sin θ = b2
= 2 cos θ sin θ = b2 - 1 ………. (iii) 

Again, from (A) we get, (sin θ/cos θ) – (cos θ/sin θ) = a 

= (sin2 θ - cos2 θ)/(cos θ sin θ) = a 
= sin2θ - cos2θ = a sin θ cos θ
= (sin θ + cos θ) (sin θ - cos θ) = a ∙ (b2 - 1)/2 ………. [by (iii)]
= b(sin θ - cos θ)= (½) a (b2 - 1) [by (ii)] 
= b2 (sin θ - cos θ)2 = (1/4) a2 (b2 - 1)2, [Squaring both the sides] 
= b2 [(sin θ + cos θ)2 - 4 sinθ cos θ] = (1/4) a2 (b2 - 1)2
= b2 [b2 - 2 ∙ (b2 - 1)] = (1/4) a2 (b2 - 1)2 [from (ii) and (iii)] 
= 4b2 (2 - b2) = a2 (b2 - 1)2

which is the required θ-eliminate.
1 5 1
Please mark it brainiest answer.....................