Advertisements
Advertisements
Question
If 3 cot A = 2, then find the value of `(4sin"A" - 3cos"A")/(2sin"A" + 3cos"A")`
Solution
3 cot A = 2
⇒ cot A = `2/3`
AC2 = AB2 + BC2
= 32 + 22
= 9 + 4
AC = `sqrt(13)`
cos A = `"AB"/"AC" = 3/sqrt(13)`
sin A = `"BC"/"AC" = 2/sqrt(13)`
The value of `(4sin"A" - 3cos"A")/(2sin"A" + 3cos"A")`
= `4(2/sqrt(13)) - 3(3/sqrt(13)) ÷ 2(2/sqrt(13)) + 3(3/sqrt(13))`
= `(8/sqrt(13)) - (9/sqrt(13)) ÷ (4/sqrt(13)) + (9/sqrt(13))`
= `((8 - 9)/sqrt(13)) ÷((4 + 9)/sqrt(13))`
= `((-1)/sqrt(13)) ÷ (3/sqrt(13))`
= `((-1)/sqrt(13)) xx (sqrt(13)/13)`
The value is `((-1)/13)`
APPEARS IN
RELATED QUESTIONS
If A = 30° B = 60° verify Sin (A + B) = Sin A Cos B + cos A sin B
If Sec 4A = cosec (A – 20°) where 4A is an acute angle, find the value of A.
If sec `theta = 17/8 ` verify that `((3-4sin^2theta)/(4 cos^2theta -3))=((3-tan^2theta)/(1-tan^2theta))`
Using the formula, sin A = `sqrt((1-cos 2A)/2) ` find the value of sin 300, it being given that cos 600 = `1/2`
From the following figure, find the values of
(i) sin B
(ii) tan C
(iii) sec2 B - tan2B
(iv) sin2C + cos2C
If cos A = `(1)/(2)` and sin B = `(1)/(sqrt2)`, find the value of: `(tan"A" – tan"B")/(1+tan"A" tan"B")`.
Are angles A and B from the same triangle? Explain.
If cosec θ = `sqrt5`, find the value of:
- 2 - sin2 θ - cos2 θ
- 2 + `1/sin^2"θ" – cos^2"θ"/sin^2"θ"`
In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD.
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
sec B = `(15)/(12)`
If cos A = `3/5`, then find the value of `(sin"A" - cos"A")/(2tan"A")`
