Question

What is the simplified value of (sin²31° + sin²59° /
sec²35° - cot²55° + tan29°cot60° - cosec²61°)

Answer 1

Answer:

use the identities

Step-by-step explanation:

sin(90-A) = cosA

tan(90-A) = cotA

sec(90-A) = cosecA

Answer 2

$\frac{sin^231^{\circ}+sin^259^{\circ}}{sec^235^{\circ}-cot^255^{\circ}+tan29^{\circ}cot61^{\circ}-cosec^261^{\circ}}=0$

Step-by-step explanation:

Given:

$\frac{sin^231^{\circ}+sin^259^{\circ}}{sec^235^{\circ}-cot^255^{\circ}+tan29^{\circ}cot61^{\circ}-cosec^261^{\circ}}$

$\frac{sin^231^{\circ}+sin^2(90-31)^{\circ}}{sec^235^{\circ}-cot^2(90-35)^{\circ}+tan(90-61)^{\circ}cot61^{\circ}-cosec^261^{\circ}}$

We know that

$tan(90-\theta)=cot\theta$

$sin(90-\theta)=cos\theta$

Using the formula

$\frac{sin^231^{\circ}+cos^231^{\circ}}{sec^235^{\circ}-tan^235^{\circ}+cot61^{\circ}cot61^{\circ}-cosec^261^{\circ}}$

$\frac{sin^231^{\circ}+cos^231^{\circ}}{sec^235^{\circ}-tan^235^{\circ}+cot^261^{\circ}-cosec^261^{\circ}}$

We know that

$sec^2\theta-tan^2\theta=1$

$cosec^2\theta-cot^2\theta=1$

$sin^2\theta+cos^2\theta=1$

Using the formula

$\frac{1}{1-1}=\frac{1}{0}=0$

$\frac{sin^231^{\circ}+sin^259^{\circ}}{sec^235^{\circ}-cot^255^{\circ}+tan29^{\circ}cot61^{\circ}-cosec^261^{\circ}}=0$

#Learn more:

https://brainly.in/question/9620628:answered by Pinquancaro