solve cos(50°+ A ) = sin (30°+ A)
pls solve
Answers
Answer:
- Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to create oxygen and energy in the form of sugar.
Answer:
Solution :-
Method-1:-
Given that
Cos (50°+A) = Sin (30°+A)
We know that
Cos (90° - A) = Sin A
=> Cos (50°+A) = Cos [90°-(30°+A)]
=> Cos (50°+A) = Cos (90°-30°-A)
=> Cos (50°+A) = Cos (60°-A)
=> 50°+A = 60°-A
Since A is acute angle
=> A+A = 60°-50°
=> 2A = 10°
=> A = 10°/2
=> A = 5°
Therefore, A = 5°
Method -2 :-
Given that
Cos (50°+A) = Sin (30°+A)
We know that
Sin (90° - A) = Cos A
=> Sin [90°-(50°+A) ]= Sin (30°+A)
=> Sin (90°-50°-A) = Sin (30°+A)
=> Sin (40°-A) = Sin (30°+A)
=> 40°-A = 30°+A
Since A is acute angle
=> A+A = 40°-30°
=> 2A = 10°
=> A = 10°/2
=> A = 5°
Therefore, A = 5°
Answer:-
The value of A for the given problem is 5°
Check:-
If A = 5° then
LHS = Cos (50°+A)
=> LHS = Cos (50°+5°)
=> LHS = Cos 55°
=> LHS = Cos (90°-35°)
=> LHS = Sin 35°
and
RHS = Sin (30°+A)
=> RHS = Sin (30°+5°)
=> RHS = Sin 35°
LHS = RHS is true for A = 5°
Verified the given relations in the given problem
Used formulae:-
→Sin (90° - A) = Cos A
→Cos (90° - A) = Sin A