The Principal Value of 𝑠𝑖𝑛⁻¹(𝑐𝑜𝑠 (33𝜋/5)) is

Which one of the following is correct?

If 𝑐𝑜𝑠⁻¹𝑥 >𝑠𝑖𝑛 ⁻¹𝑥,𝑡ℎ𝑒𝑛

If θ= t𝑎𝑛⁻¹ a,∅= 𝑡𝑎𝑛⁻¹ 𝑏 and ab = -1 then (θ− ∅) is equal to

If 𝑐𝑜𝑠⁻¹ (3/5 )−𝑠𝑖𝑛⁻¹( 4/5) = 𝑐𝑜𝑠⁻¹ 𝑥,then 𝑥 is equal to

The domain of the function defined by f(x) = 𝑠𝑖𝑛⁻¹√𝑥−1 𝑖𝑠

The domain of the function 𝑐𝑜𝑠⁻¹( 2x-1) is

If 3 𝑡𝑎𝑛⁻¹ 𝑥+ 𝑐𝑜𝑡⁻¹ 𝑥 = 𝜋 then x is equal to

The value of sin [(𝜋/2)− 𝑠𝑖𝑛 ⁻¹ (−√3/2)] is

The value of tan {𝑐𝑜𝑠⁻¹(−2/7 ) - 𝜋/2 } is

The value of the expression 2 𝑠𝑒𝑐⁻¹ 2+𝑠𝑖𝑛⁻¹(1/2) 𝑖𝑠

If 𝑡𝑎𝑛⁻¹𝑥+𝑡𝑎𝑛⁻¹ 𝑦=4𝜋/5, then 𝑐𝑜𝑡⁻¹𝑥+𝑐𝑜𝑡⁻¹𝑦 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜

The value of cot[𝑐𝑜𝑠⁻¹(7/25) ] 𝑖𝑠

The value of 𝑡𝑎𝑛⁻¹(𝑡𝑎𝑛(5𝜋/6))+𝑐𝑜𝑠⁻¹(𝑐𝑜𝑠(13𝜋/6)) 𝑖𝑠

The simplified form of cos[𝑐𝑜𝑠⁻¹(−√3/2)+ (𝜋/6) ] is

The value of 𝑡𝑎𝑛⁻¹(−1/√3)+𝑐𝑜𝑡⁻¹(1/√3)+𝑡𝑎𝑛⁻¹(sin(−𝜋/2)) is

𝑠𝑖𝑛⁻¹𝑥+𝑠𝑖𝑛⁻¹(1/𝑥)+𝑐𝑜𝑠⁻¹𝑥+𝑐𝑜𝑠⁻¹(1/𝑥),  𝑥∉±1 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜

   The simplified form of 𝑐𝑜𝑠⁻¹((3/5)𝑐𝑜𝑠 𝑥+(4/5)𝑠𝑖𝑛 𝑥) 𝑤ℎ𝑒𝑟𝑒 𝑥∈[−3𝜋/4,𝜋/4 ] 𝑖𝑠

The value of x for which 𝑐𝑜𝑠⁻¹(𝑐𝑜𝑠 4)>3𝑥²−4𝑥 is

If tan (𝑐𝑜𝑠⁻¹𝑥)=sin(𝑐𝑜𝑡⁻¹(1/2)),𝑡ℎ𝑒𝑛 𝑥 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜

If 𝑐𝑜𝑠⁻¹𝑥+𝑐𝑜𝑠⁻¹𝑦=𝜋/2 𝑎𝑛𝑑 𝑡𝑎𝑛⁻¹𝑥−𝑡𝑎𝑛⁻¹ 𝑦=𝜋/4     𝑡ℎ𝑒𝑛 𝑥²+𝑥𝑦+𝑦² 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜

The solution of 𝑡𝑎𝑛⁻¹2𝑥 +𝑡𝑎𝑛⁻¹3𝑥=𝜋/4 is

The value of sin {2 𝑡𝑎𝑛⁻¹(.75)} is equal to

If 𝑠𝑖𝑛⁻¹ (2𝑎/(1+𝑎²))+co𝑠⁻¹ ((1−𝑎²)/(1+𝑎²))=ta𝑛⁻¹(2𝑥/(1−𝑥²)) where a, x ∈[0,1],𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 𝑖𝑠

If we consider only the principal values of the inverse trigonometric functioned then the value of tan(co𝑠⁻¹( 1/5√2) - si𝑛⁻¹ (4/√17)) is