If sin x = 3/5 , cos y = − 12/13 , where x and y both lie in second

1.	If sin x = 3/5 , cos y = − 12/13 , where x and y both lie in second quadrant, find the value of sin (x + y).
Answer» We know that sin (x + y) = sin x cos y + cos x sin y ... (1) Now cos²x = 1 – sin²x = 1 – 9/25 = 16/25 Therefore cos x = ± 4/5. Since x lies in second quadrant, cos x is negative. Hence cos x = −4/5 Now sin²y = 1 – cos²y = 1 – 144/169 = 25/169 i.e. sin y = ± 5/13. Since y lies in second quadrant, hence sin y is positive. Therefore, sin y =5/13. Substituting the values of sin x, sin y, cos x and cos y in (1), we get sin(x + y) 3/5 × (-12/13) + (−4/5) × 5/13 = (-36/65) –(20/65) = -56/65 Therefore, sin(x+y) = -56/65

If sin x = 3/5 , cos y = − 12/13 , where x and y both lie in second quadrant, find the value of sin (x + y).

Answer»

We know that
sin (x + y) = sin x cos y + cos x sin y ... (1)
Now cos²x = 1 – sin²x = 1 – 9/25 = 16/25
Therefore cos x = ± 4/5.
Since x lies in second quadrant, cos x is negative.
Hence cos x = −4/5
Now sin²y = 1 – cos²y = 1 – 144/169 = 25/169
i.e. sin y = ± 5/13.
Since y lies in second quadrant, hence sin y is positive.

Therefore, sin y =5/13.

Substituting the values of sin x, sin y, cos x and cos y in (1), we get
sin(x + y) 3/5 × (-12/13) + (−4/5) × 5/13 = (-36/65) –(20/65) = -56/65

Therefore, sin(x+y) = -56/65

Discussion

No Comment Found

Related InterviewSolutions

The value of (cot30^(@)-cot75^(@))/(tan15^(@)-tan60^(@)))` is
The expression `(tan57^(@)-cot75^(@))/(tan15^(@)-tan60^(@))` isA. `tan30^(@)cot57^(@)`B. `tan57^(@)cot37^(@)`C. `tan33^(@)cot53^(@)`D. `tan33^(@)cot37^(@)`
यदि `sin7x=cos11x`, है तो `tan9x+cot9x` का मान है?A. 1B. 2C. 3D. 4
यदि `tan15^(@)=2-sqrt(3)`, है तो `tan15^(@)cot75^(@)+tan75^(@)cot15^(@)` का मान ज्ञात करे?A. 14B. 12C. 10D. 8
`tan10^(@)" "tan15^(@)" "tan75^(@)" "tan80^(@) `का मान है?
Consider the following statements:I. -1 ≤ sinn θ ≤ 1 where n is odd integerII. -1 ≥ Cosecn θ ≥ 1 where n is odd integerFind which statement is/are correct?1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2
An observer 1.6 m tall is 20√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: 1. 21.6 m2. 23.2 m3. 24.72 m4. None of these
If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the angles A, B and C respectively. If \(s=\dfrac{a+b+c}{2}=6\), then the product \(\dfrac{1}{3}s^2 (s-a)(s-b)(s-c)\) is equal to 1. 2Δ 2. 2Δ23. \(\sqrt{2}\Delta\)4. Δ2
If α and β are positive angles such that \(α + β = \dfrac{\pi}{4}\), then what is (1 + tan α) (1 + tan β) equal to?
What is the value of \(\sin^{-1} \frac{4}{5} + 2 \tan^{-1} \frac{1}{3} \ ?\)1. \(\dfrac{\pi}{3}\)2. \(\dfrac{\pi}{2}\)3. \(\dfrac{\pi}{4}\)4. \(\dfrac{\pi}{6}\)