Question

please help me .i am ritesh kumar from Bihar​

Answer 1

(6) We know that

Sin⁻¹x + Cos⁻¹x = π / 2

=> Cos⁻¹x =( π / 2) - Sin⁻¹x

Now

Cos⁻¹x + Cos⁻¹y

= (π/2 - Sin⁻¹x )+( π/2 - Sin⁻¹y)

=( π/2 + π/2) - (Sin⁻¹x + Sin⁻¹y )

= π - ( 2π / 3 )

= ( 3π -2 π / 3 )

= π / 3

So option C is correct

(7) We know that

1 + tan²θ = Sec²θ

1 + Cot²θ = Cosec²θ

tan⁻¹ (tanθ) = θ

Cot⁻¹(Cotθ) = θ

Now

Sec² (tan⁻¹ 5 ) + Cosec² ( Cot⁻¹ 5 )

=1 + tan² (tan⁻¹5 ) + 1 + Cot² ( Cot⁻¹ 5 )

=2 +{ tan (tan⁻¹5) }² + { Cot (Cot⁻¹5) }²

=2 + ( 5 )² + ( 5 )²

= 2 + 25 + 25

= 52

Option D is correct

(8) Cos⁻¹(1/2) + 2 Sin⁻¹(1/2)

= Cos⁻¹ (Cos π/3 ) + 2 Sin⁻¹ ( Sin π/6 )

= π / 3 + 2 ( π / 6 )

= π / 3 + π / 3

= 2 π / 3