Trigonometry question in photo 10 grade cbse question
Answers
Solution:-
Given:-
tanθ = 20/21
To Prove:-
[ ( 1-sinθ + cosθ) / ( 1 + sinθ + cosθ ) ] = 3/7
Proof :-
Let the sides of the Triangle be "x".
We know that,
tanθ = Perpendicular/ Base
=) tanθ = Perpendicular/Base = 20/21
Hence,
Perpendicular = 20x
Base = 21x
By Pythagoras Theorem,
Hypotenuse² = Perpendicular² + Base²
=) H² = ( 20x )² + ( 21x )²
=) H² = 400x² + 441x²
=) H = √841x²
=) H = 29x
Hence,
Hypotenuse = 29x
Now, Finding the value of sinθ and cosθ.
sinθ = Perpendicular/Hypotenuse
=) sinθ = 20x / 29x
=) sinθ = 20/29
cosθ = Base / Hypotenuse
=) cosθ = 21x / 29x
=) cosθ = 21/29
Substituting the values of "sinθ" and "cosθ" in the Equation. We get,
=) [ ( 1 - 20/29 + 21/29 ) / ( 1 + 20/29 + 21/29 ) ]
=) [ ( 29 - 20 + 21 ) / ( 29 + 20 + 21 ) ]
=) 30/70
=) 3/7
Hence Proved!
Answer:
No answer. Just check the explanation...
Step-by-step explanation:
Let θ = A.
Then, tanA = Perp./Base = 20/21
Let P = 20k and B = 21k.
Now, By Pythagoras theorem,
H = √k²(20²+ 21²) = k√400+441 = 29k
sinA = P/H = 20k/29k = 20/29
cosA = B/H = 21k/29k = 21/29
To Prove:-
(1 - sinA + cosA)/(1 + sinA + cosA) = 3/7
Taking LHS:
(1 - sinA + cosA)/(1 + sinA + cosA)
= (1 - 20/29 + 21/29)/(1 + 20/29 + 21/29)
= (29 - 20 + 21/29)(29 + 20 + 21/29)
= (50-20)/(70)
= 30/70
= 3/7
= RHS
LHS = RHS
Hence Proved.