# If evaluate:(i) (ii) Let us consider a right triangle ABC, right-angled at point B Given: As, a trigonometric Ratio shows the ratio between different sides, cot also shows the ratio of Base and Perpendicular. As we don't know the absolute value of Base and Perpendicular, let the base and perpendicular be multiplied by a common term, let it be k
Therefore,
Base = 7 k
Perpendicular = 8k
According to pythagoras theorem,
(Hypotenuse)2 = (Base)+ (Perpendicular)2

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

= (8k)2 + (7k)2

= 64k2 + 49k2

= 113k2

AC = √113 k

Now we have all the three sides of the triangle,
Base = 7 k
Perpendicular = 8 k
Hypotenuse = √113 k
Now applying other trigonometric angle formulas Sin = = =  Cos θ = = = (i) Putting the obtained trigonometric ratios into the expression we get,
= (1 – sin2 θ)/(1 – cos2 θ) = 49/64

(ii) Cot2 θ = (cot θ)2 Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Trigonometric Identities44 mins  Champ Quiz | Trigger on Trigonometry47 mins  Basics of TrigonometryFREE Class  NCERT | Imp. Qs. Discussion - Trigonometry44 mins  Smart Revision | Trigonometric Ratios41 mins  NCERT | Imp. Qs. on Trigonometry42 mins  Quiz | Trail of Mixed Questions on Trigonometry59 mins  Champ Quiz | NTSE Trigonometry50 mins  Testing the T- Ratios of Specified Angles57 mins  Foundation | Cracking Previous Year IMO Questions59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 