# Prove that:</

(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

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