If sin (A + B) = 1 and cos (A – B) = 1, find A and B.

Given : sin (A+B) =1

Sin(A+B) = sin (90 o) [ sin (90 o) =1]

On equating both the sides, we get

A + B = 90 o …(1)

And cos (A – B) = 1

cos(A B) = cos (0 o) [ cos(0 o) = 1]

On equating both the sides, we get

A – B = 0 o …(2)

On Adding Eq. (1) and (2), we get

2A = 90 o

A = 45 o

Now, Putting the value of A in Eq.(1), we get

45 o + B =90 o

B = 45 o

Hence, A = 45 o and B = 45 o

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Identities33 mins
Champ Quiz | Trigonometric Identities33 mins
NCERT | Trigonometric Identities52 mins
Quiz | Task on Trigonometric Ratios46 mins
Trigonometric Identities44 mins
Solving NCERT Questions on Trigonometric Identities56 mins
Algebraic Identities48 mins
Quiz | Practice Important Questions on Trigonometrical Identities46 mins
Quiz on Trigonometric Ratios31 mins
T- Ratios of Specified Angles58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses