Question

sec^2(25+∅)-Co sec^2(65-∅)+(Cos^240°+co sec^238°) / (sin^250°+sec^252°) + (sec 57°.sin 64°) / ( co sec 33°.cos 26°)

Answer 1

Answer:

- cos2 A) cosec2 A = 1

Solution:

(1 - cos2 A)cosec2 A

= Sin2 A cosec2 A

= (Sin A cosec A)2

= (Sin A × (1/Sin A))2

= (1)2

= 1

Question: 2

(1 + Cot2 A) Sin2 A = 1

Solution:

We know,

cosec2A - Cot 2 A = 1

So, (1 + Cot2 A) Sin2 A

= Cosec2 A Sin2 A

= (Cosec A Sin A)2

= ((1/Sin A) × Sin A)2

= (1)2

= 1

Question: 3

tan2θ cos2θ = 1 − cos2θ

Solution:

We know,

sin2 θ + cos2 θ = 1

So, tan2 θ cos2 θ

= (tan θ × cos θ)2

= (sin θ)2 sin2θ 1 - cos2θ

Question: 4

Solution:

We know,

sin2 θ + cos2 θ = 1

= 1

Question: 5

(sec2θ − 1)(cosec2θ − 1) = 1

Solution:

We know that, (sec2θ − tan2θ) = 1 (cosec2θ − cot2θ) = 1

So, (sec2θ - 1)(cosec2θ - 1)

= tan2θ × cot2θ

= (tan θ × cot θ)2

= 12

= 1

Question: 6

Solution:

We know that, (sec2θ − tan2θ) = 1

So,

Question: 7

Solution:

We know, sin2θ + cos2θ = 1

So, Multiplying both numerator and denominator by (1+ sin θ), we have