This is the basic and conceptual question from trigonometric ratios in which we have been asked to calculate the value of angle A and B, if sin (A + B) = 1 and cos (A − B) = 1, 0° ≤ (A + B) ≤ 90° and A > B.
RS Aggarwal, Class 10, chapter 11, question no 23
Given, sin(A+B)=1
cos(A−B)=1
0∘<A+B≤90∘ and A≥B,
We know that, sin90∘=1 and cos0∘=1
Consider,
sin(A+B)=1 and sin90∘=1
⟹(A+B)=90∘ —————(i)
Consider,
cos(A−B)=1 and cos0∘=1
⟹(A−B)=0∘
⇒A=B —————(ii)
sub (ii) in (i)
A+A=90∘
⇒2A=90∘
⇒A=45∘
⇒A=B=45∘
∴A=B=45∘