please solve all questions class 10 exercise 8.2
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Answer:
Step-by-step explanation:
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2. (i) 2tan30°/1+tan^2 30°
=2×1/√3 /1+(1/√3)^2
=2/√3 /1+1/3
=2/√3 /4/3
=2/√3×3/4
=3/2√3×√3/√3
=3√3/2×3
=√3/2 = sin60° (a)
(ii) 1-tan^2 45°/1+tan^2 45°
=1-(1)^2 /1+(1)^2
=1-1/1+1
=0/2 = 0 (d)
(iii) sin2A = 2sinA
sin2×0 = 2sin0
0 = 0 (a)
(iv) 2tan30°/1-tan^2 30°
=2×(1/√3) / 1-(1/√3)^2
=2/√3 / 1-1/3
=2/√3 / 2/3
=2/√3 × 3/2
=3/√3×√3/√3
=3√3/3
=√3 = tan60° (c)
3. tan(A+B) = √3 , 0°
tan(A-B) = 1/√3 , A-B=90°
A+B = 60° ___________(i)
A-B = 30° ___________(ii)
from eq (i) and (ii),
2A = 90°
A = 45°
from eq (i),
A+B = 60°
45°+B = 60°
B = 60° - 45°
B = 15°