(cos9°+sin9°)(cos9°-sin9°) is equal to
tan26°
tan81°
tan51°
tan54°
tan46°
Explanation or the correct option:
Solve the expression (cos9°+sin9°)(cos9°–sin9°)
By Divide the numerator and denominator by cos 9°, we get
cos9°cos9°+sin9°cos9°cos9°cos9°–sin9°cos9°
=(1+tan9°)(1–tan9°)
=(tan45°+tan9°)[1–tan9°×(1)] ; ∵tan45°=1
=(tan45°+tan9°)(1–tan9°tan45°)
=tan(45°+9°) ; ∵tanA+tanB1-tanAtanB=tan(A+B)
=tan54°
Hence, Option ‘D’ is Correct.