The Total solution for NCERT class 6-12
Prove the following results:
(i) 2 sin-1 (3/5) = tan-1 (24/7)
(ii) tan-1 ¼ + tan-1 (2/9) = ½ cos-1 (3/5)= ½ sin-1 (4/5)
(iii) tan-1 (2/3) = ½ tan-1 (12/5)
(iv) tan-1 (1/7) + 2 tan-1 (1/3) = π/4
(v) sin-1 (4/5) + 2 tan-1 (1/3) = π/2
(vi) 2 sin-1 (3/5) – tan-1 (17/31) = π/4
(vii) 2 tan-1 (1/5) + tan-1 (1/8) = tan-1 (4/7)
(viii) 2 tan-1 (3/4) – tan-1 (17/31) =π/4
(ix) 2 tan-1 (1/2) + tan-1 (1/7) = tan-1 (31/17)
(x) 4 tan-1(1/5) – tan-1(1/239) = π/4
(i) Given 2 sin-1 (3/5)= tan-1 (24/7)
Hence, proved.
(ii) Given tan-1 ¼+ tan-1 (2/9) = ½ cos-1 (3/5) = ½ sin-1 (4/5)
(iii) Given tan-1 (2/3)= ½ tan-1 (12/5)
(iv) Given tan-1 (1/7)+ 2 tan-1 (1/3) = π/4
(v) Given sin-1 (4/5)+ 2 tan-1 (1/3) = π/2
(vi) Given 2 sin-1 (3/5)– tan-1 (17/31) = π/4
(vii) Given 2 tan-1 (1/5)+ tan-1 (1/8) = tan-1 (4/7)
(viii) Given 2 tan-1 (3/4)– tan-1 (17/31) = π/4
(ix) Given 2 tan-1 (1/2)+ tan-1 (1/7) = tan-1 (31/17)
(x) Given 4 tan-1(1/5)– tan-1(1/239) = π/4