Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) (tan⁵x + tan⁷x)sec²x A)sec4x tan¹²x B)sec4x tan⁵x C)7 sec4x tan⁵x D)5 sec4x tan⁵x E)sec12x tan⁵x

Question

Quizplus · Accepted Answer

We will use the identity: 
tan(A + B) = (tanA + tanB)/(1 - tanA tanB)

So, 
tanS1U1P15S1S1P0x + tanS1U1P17S1S1P0x = (tanS1U1P15S1S1P0x + tanS1U1P15S1U1P2S1P0x)/(1 - tanS1U1P15S1S1P0x tanS1U1P15S1U1P2S1P0x)

= tanS1U1P15S1U1P1S1P0x  secS1U1P12S1S1P0x

Putting this in the original expression, we get:

(tanS1U1P15S1U1P1S1P0x  secS1U1P12S1S1P0x ) secS1U1P12S1S1P0x

sec2S1U1P12S1S1P0x tanS1U1P15S1U1P1S1P0x

= sec4x tanS1U1P15S1S1P0x

Therefore, the answer is B.

Evaluate the Following Expression