Answer :

(i)

we know, 
tan(90 - A) = cot A
and cotA tanA = 1

By using above concepts, we can solve the question as:

Consider LHS,

tan20°tan35°tan45°tan55°tan70°=tan(90°-70°)tan(90°-55°)tan45°tan55°tan70°

⇒ tan20°tan35°tan45°tan55°tan70°=cot70°cot55°tan45°tan55°tan70°

⇒ tan20°tan35°tan45°tan55°tan70°=(cot70°tan70°)(cot55°tan55°)tan45°

Since tan45°=1,

⇒ tan20°tan35°tan45°tan55°tan70°=1×1×1

Which is equal to RHS.

Hence Proved


(ii)

we know, 
sec(90 - A) = cosec A
and sinA.cosecA = 1

By using above concepts, we can solve the question as


Proved

(iii)

we know, 
sin(90 - A) = cos A and
cosec(90 - A) =  sec A, By using this information we can solve our question as


Proved

(iv)

we know, 
sin(90 - A) = cos A and
cosec(90 - A) =  sec A, By using this information we can solve our question as

Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric IdentitiesTrigonometric IdentitiesTrigonometric Identities39 mins
Trigonometric Identities-IITrigonometric Identities-IITrigonometric Identities-II43 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
caricature
view all courses
RELATED QUESTIONS :

At a point A, 20 Mathematics - Board Papers

If <img style="veRD Sharma - Mathematics

From a point on tMathematics - Board Papers

Evaluate each of RD Sharma - Mathematics

Express <imRD Sharma - Mathematics