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Hi there!
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ POINTS TO REMEMBER:
¶ SIN = OPPOSITE/HYPOTENUSE
¶ COS = ADJACENT/HYPOTENUSE
¶ TAN = OPPOSITE/ ADJACENT
¶ According to Pythagoras theorem,
HYP² = ADJ² + OPP²
¶ (a+b)² - (a-b)² = 4ab
{ (a² + b² +2ab) - (a² + b² - 2ab)
= a² + b² +2ab - a² - b² + 2ab
= 4ab}
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ SOLUTION:
Taking theta as 'a'
Given,
Sin a = (x² - y²)/(x²+y²)
Here,
Opp = (x² - y²) & Hyp =(x²+y²)
Using Pythagoras theorem, find the other side
Let Adj be 'A'
=> (x²+y²)² = (x²-y²)² + A²
=> A² = (x²+y²)² - (x²-y²)²
=> A² = 4x²y²
{Here, a= x² ; b = y²}
=> A = √ 4x²y²
=> A = 2xy
•°• Adj = 2xy
Adj = 2xy ; Opp = (x² - y²) & Hyp =(x²+y²)
Now, we have all sides
So any trigonometric ratio can be found
(1)
cos a = 2xy/(x²+y²)
(2)
tan a = (x²-y²)/2xy
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Hope it helps
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ POINTS TO REMEMBER:
¶ SIN = OPPOSITE/HYPOTENUSE
¶ COS = ADJACENT/HYPOTENUSE
¶ TAN = OPPOSITE/ ADJACENT
¶ According to Pythagoras theorem,
HYP² = ADJ² + OPP²
¶ (a+b)² - (a-b)² = 4ab
{ (a² + b² +2ab) - (a² + b² - 2ab)
= a² + b² +2ab - a² - b² + 2ab
= 4ab}
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ SOLUTION:
Taking theta as 'a'
Given,
Sin a = (x² - y²)/(x²+y²)
Here,
Opp = (x² - y²) & Hyp =(x²+y²)
Using Pythagoras theorem, find the other side
Let Adj be 'A'
=> (x²+y²)² = (x²-y²)² + A²
=> A² = (x²+y²)² - (x²-y²)²
=> A² = 4x²y²
{Here, a= x² ; b = y²}
=> A = √ 4x²y²
=> A = 2xy
•°• Adj = 2xy
Adj = 2xy ; Opp = (x² - y²) & Hyp =(x²+y²)
Now, we have all sides
So any trigonometric ratio can be found
(1)
cos a = 2xy/(x²+y²)
(2)
tan a = (x²-y²)/2xy
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Hope it helps
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