In a right angled triangle ABC, right angled at B, given 15 cos A - 8 Sin A = 0,
1. Sin A + Cos A / 2 Cos A - Sin A = ?
2. 15 cot A + 17 sin A / 2 Cos A - Sin A = ?
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Answers
Step-by-step explanation:
Given:-
In a right angled triangle ABC, right angled at B, given 15 cos A - 8 Sin A = 0.
To find:-
Find the following:
1. Sin A + Cos A / 2 Cos A - Sin A = ?
2. 15 cot A + 17 sin A / 2 Cos A - Sin A = ?
Solution:-
Given that
15 cos A - 8 Sin A = 0
=> 15 Cos A = 8 Sin A
=> Cos A / Sin A = 8/15
=> Cot A = 8/15-------(1)
On squaring both sides
=> Cot^2 A = (8/15)^2
=> Cot^2 A = 64/225
Now
=> 1+Cot^2 A = 1+(64/225)
=> 1+ Cot^2 A = (225+64)/225
=> 1+Cot^2 A = 289/225
We know that
Cosec^2 A - Cot^2 A = 1
=> Cosec^2 A = 1+Cot^2 A
=> Cosec^2 A = 289/225
=> Cosec A = √(289/225)
=> Cosec A = 17/15
Sin A = 15/17---------(2)
On squaring both sides
=> Sin^2 A = 225/289
=> 1- Sin^2 A = 1-(225/289)
=> 1-Sin^2 A = (289-225)/289
=> 1- Sin^2 A = 64/289
We know that
Sin^2 A + Cos^2 A = 1
=> Cos^2 A = 64/289
=> Cos A =√(64/289)
Cos A = 8/17-----------(3)
I) The value of
(Sin A + Cos A) / (2 Cos A - Sin A )
=>[ (15/17)+(8/17)]/[2(8/17)-(15/17)]
=>[ (15+8)/17 ]/ [ (16-15)/17]
=> (23/17)/(1/17)
=> 23/1
=>23
(Sin A + Cos A) / (2 Cos A - Sin A ) = 23
2) The value of
(15 cot A + 17 sin A) / (2 Cos A - Sin A)
=> [15(8/15)+17(15/17)] /[ 2(8/17)-(15/17)]
=> [(15×8/15)+(17×15/17)] / [(2×8/17)-(15/17)]
=> (8+15)/ [(16/17)-(15/17)]
=> 23/[(16-15)/17]
=> 23/(1/17)
=> 23×(17/1)
=> 23×17
=> 391
(15 cot A + 17 sin A) / (2 Cos A - Sin A) = 391
Answer:-
The values of
i)(Sin A + Cos A) / (2 Cos A - Sin A ) = 23
ii)(15 cot A + 17 sin A) / (2 Cos A - Sin A) = 391
Used formulae:-
- Cosec^2 A - Cot^2 A = 1
- Sin^2 A + Cos^2 A = 1
- Cot A = Cos A / Sin A
- Cosec A = 1/ Sin A
Answer:
find:
Find the following:
1. Sin A+ Cos A/2 Cos A- Sin A = ?
2. 15 cot A+ 17 sin A/2 Cos A - Sin A = ?
Solution:
Given that
15 cos A-8 Sin A 0
=> 15 Cos A = 8 Sin A
=> Cos A/Sin A = 8/15
=> Cot A = 8/15-----(1)
On squaring both sides
=>Cot^2 A (8/15) 2
=> Cot^2 A 64/225
Now
1+Cot^2 A 1+(64/225)
=> 1+ Cot^2 A = (225+64)/225
> 1 => 1+Cot 2 A = 289/225
We know that
Cosec^2 A - Com^2 A=1
=> Cosec^2 A=1+Cot^2 A
=> Cosec^2 A = 289/225
Cosec A=√(289/225)
=> Cosec A = 17/15
Sin A 15/17-------(2)
On squaring both sides
=> Sin^2 A = 225/289
=> 1- Sin^2 A1-(225/289)
=> 1-Sin^2 A = (289-225)/289
=>1- Sin 2 A = 64/289
We know that
Sin^2 A+ Cos^2 A = 1
=> Cos^2 A 64/289)
=> Cos A =√(64/289)
Cos A8/17 (3)
1) The value of
(Sin A+ Cos A) / (2 Cos A - Sin A)
=>(15/17)+(8/17)]/[2(8/17)-(15/17)]
(15+8)/17 (16-15)/17]
=>(23/17)/(1/17)
=> 23/1
=>23
(Sin A+ Cos A) / (2 Cos A Sin A ) = 23
2) The value of
(15 cot A+ 17 sin A) / (2 Cos A - Sin A)
=> [15(8/15)+17(15/17)] /[2(8/17)-(15/17)]
=> [(15-8/15)+(17*15/17)] / [(2*8/17)-(15/17)]
(8+15)/ [(16/17)-(15/17)]
=> 23/[(16-15)/17]
=> 23/(1/17)
=> 23×(17/1)
=> 23×17
=> 391
(15 cot A+ 17 sin A) / (2 Cos A - Sin A) = 391
Answer:
The values of
i)(Sin A+ Cos A) / (2 Cos A - Sin A ) = 23
ii)(15 cot A + 17 sin A) / (2 Cos A- Sin A) = 391
Used formulae:
. Cosec^2 A - Cot^2 A = 1
• Sin^2 A+ Cos^2 A = 1
• Cot A = Cos A / Sin A
• Cosec A = 1/ Sin A
Step-by-step explanation:
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