Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Prove the following : {(90^{} , - , A) , , A}{^2 , A} , - ,

Question

Prove the following :

$\frac{tan ( 9 0 ^{\circ} - A ) cot A}{csc ^{2} A} - cos^{2} A = 0.$

Views: 908 students

Found 6 tutors discussing this question

Mia Discussed

Prove the following :

\frac{tan ( 9 0 ^{\circ} - A ) cot A}{csc ^{2} A} - cos^{2} A = 0.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

L.H.S

= \frac{tan ( 9 0 ^{\circ} - A ) cot A}{csc ^{2} A} - cos^{2} A

We know that,

cos (90 - θ) = sin θ

sin (90 - θ) = cos θ

tan (90 - θ) = cot θ

cot θ = \frac{cos θ}{sin θ}

csc θ = \frac{1}{sin θ}

= \frac{cot ( A ) cot A}{csc ^{2} A} - cos^{2} A

= \frac{cot ^{2} A}{csc ^{2} A} - cos^{2} A

= \frac{( \frac{cos ^{2} A}{sin ^{2} A} )}{( \frac{1}{sin ^{2} A} )} - cos^{2} A

= cos^{2} A - cos^{2} A

= 0

=R.H.S

∵ \frac{tan ( 9 0 ^{\circ} - A ) cot A}{csc ^{2} A} - cos^{2} A = 0

hence proved

Was this solution helpful?

150

Share

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Essay review

Get expert feedback on your essay

Schedule classes

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Doubt Icon

Doubt Icon

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Prove the following : $\frac{tan ( 9 0 ^{\circ} - A ) cot A}{csc ^{2} A} - cos^{2} A = 0.$
Answer Type	Text solution:1
Upvotes	150