Question

prove that the trigonometry identities whole root sec²∅+cosec²∅ = tan∅+cot∅​

Answer 1

Step-by-step explanation:

$sec^2\alpha +cosec\alpha ^{2} =1/cos^2\alpha +1/sec^{2} \alpha$

Taking LCM

$cos^{2} \alpha +sin^{2}\alpha/sin^{2} \alpha cos^2\alpha \\sin^2\alpha+cos^2\alpha=1\\so 1/cos^2\alpha sin^2\alpha\\Taking root\\1/sin\alpha cos\alpha$

First equation

$sin\alpha/cos\alpha + cos\alpha/sin\alpha$

Taking LCM

$sin^2\alpha+cos^2\alpha/sin\alpha cos\alpha\\\\so\\1/sin\alpha+cos\alpha$

Equation 2

Equation 1 and 2 are equal so proved

Answer 2

Answer:

given that: sec²ø + cosec²ø

TO PROVE: tanø + cotø

sec²ø = 1 + tan²ø

cosec²ø = 1 + cot²ø

So, Now we can write sec²ø + cosec²ø as:

1 + tan²ø + 1 + cot²ø

= 1 + sin²ø/cos² ø + 1 + cos²ø/sin²ø

= 2 + sin²ø/cos²ø + cos²ø/sin²ø

= 2 + sin²ø