If tan θ=√( a / b ) where a , b are positive reals then the value of sin θ sec 7 θ+ cos θ textcosec7 θ is -

Question

If tan θ=√( a / b ) where a , b are positive reals then the value of sin θ sec 7 θ+ cos θ textcosec7 θ is - (A) ((a+b)3(a4+b4)/(a b)7 / 2) (B) ((a+b)3(a4-b4)/(a b)7 / 2) (C) ((a+b)3(b4-a4)/(a b)7 / 2) (D) -(( a + b )3( a 4+ b 4)/( ab )7 / 2)

Tardigrade Admin · Accepted Answer

Correct answer is (a) ((a+b)3(a4+b4)/(a b)7 / 2)

Q. If $tan θ = \frac{a}{b}$ where $a, b$ are positive reals then the value of $sin θ sec^{7} θ + cos θ cosec^{7} θ$ is -

$\frac{( a + b ) ^{3} ( a ^{4} + b ^{4} )}{( ab ) ^{7/2}}$

$\frac{( a + b ) ^{3} ( a ^{4} - b ^{4} )}{( ab ) ^{7/2}}$

$\frac{( a + b ) ^{3} ( b ^{4} - a ^{4} )}{( ab ) ^{7/2}}$

$- \frac{( a + b ) ^{3} ( a ^{4} + b ^{4} )}{( ab ) ^{7/2}}$

Correct answer is (a) $\frac{( a + b ) ^{3} ( a ^{4} + b ^{4} )}{( ab ) ^{7/2}}$

Q. If tanθ=ba​​ where a,b are positive reals then the value of sinθsec7θ+cosθcosec7θ is -

(ab)7/2(a+b)3(a4+b4)​

(ab)7/2(a+b)3(a4−b4)​

(ab)7/2(a+b)3(b4−a4)​

−(ab)7/2(a+b)3(a4+b4)​