Question

Case study: If x and y are in second quadrant and Sin x = 5/13 , Tan y = -3/4 then answer the following ? Cos x = 12/13 b) -12/13 c) 13/12 d) -13/12 Cos y = -4/5 b) 4/5 c) 3/5 d) -3/5 Sin (x+y) = 56/65 b) -56/65 c) -55/64 d) 55/64 Cos (x-y) = 62/65 b) -62/65 c) 63/65 d) 64/65​

Answer 1

Answer:

please check your question

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Answer 2

Answer:

1) The correct answer is option(b)  $\frac{-12}{13}$

2) The correct answer is option(a)   $\frac{-4}{5}$

3) The correct answer is option(b)  $\frac{-56}{65}$

4) The correct answer is option(c) $\frac{63}{65}$

Step-by-step explanation:

Given,

x and y are in second quadrant

Sin x = $\frac{5}{13}$ , Tan y =$\frac{-3}{4}$

(1)  To find,

The value of cos x

Given Sin x = $\frac{5}{13}$,

we have,

sinx = $\frac{Opposite\ side }{hypotenuse}$

Opposite side = 5x and hypotenuse = 13x

adjacent side²  = (13x)² - (5x)²  = 169x² - 25x² = 144x²

adjacent side = 12x

cos x = $\frac{adjacent\ side }{hypotenuse}$ = $\frac{12x}{13x} = \frac{12}{13}$

Since 'x' is in the second quadrant, the value of cos is negative

Hence cos x = $\frac{-12}{13}$

The correct answer is option(b)

(2) To find

The value of Cos y

Given, tan y =$\frac{-3}{4}$

we have, tan y = $\frac{Opposite\ side }{adjacent \ side}$

Opposite side = 3x and adjacent side = 4x

Hypotenuse = (3x)² + (4x)²  = 9x² +16x² = 25x²

hypotenuse = 5x

cos y = $\frac{adjacent \ side }{hypotenuse}$ = $\frac{4x}{5x} = \frac{4}{5}$

Since 'y' is in the second quadrant, the value of cos is negative

Hence cos y = $\frac{-4}{5}$

The correct answer is option(a)

3) To find,

The value of sin(x+y)

We know sin(x+y) = sinx cosy + cosx siny

Sin x = $\frac{5}{13}$, cosy = $\frac{-4}{5}$,  cos x = $\frac{-12}{13}$, sin y = $\frac{3}{5}$

sin(x+y) = $\frac{5}{13}$× $\frac{-4}{5}$ + $\frac{-12}{13}$ × $\frac{3}{5}$

=$\frac{-20}{65}+\frac{-36}{65}$

= $\frac{-56}{65}$

sin(x+y) = $\frac{-56}{65}$

The correct answer is option(b)

4)To find,

The value of cos(x-y)

We know, cos(x-y)  = cosx cosy+sinx siny

Sin x = $\frac{5}{13}$, cosy = $\frac{-4}{5}$,  cos x = $\frac{-12}{13}$, sin y = $\frac{3}{5}$

cos(x-y) = $\frac{-12}{13}$ × $\frac{-4}{5}$ + $\frac{5}{13}$ × $\frac{3}{5}$

= $\frac{63}{65}$

cos(x-y) = $\frac{63}{65}$

The correct answer is option(c)

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