Question

Cosec257 – tan233 =? a. 0 b. 1 c. -1 d. 2

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

$\sf{Cosec^{2} 57 - tan^{2} 33}$

$\sf{= Cosec^{2} (90-33) - tan^{2} 33}$

$\sf{= Sec^{2} 33 - tan^{2} 33}$

$\sf{= (1 + tan^{2} 33 - tan^{2} 33)}$

$\sf{= \: 1}$

Using Identities :-

1)$\sf{Cosec(90 - O) = SecO}$

2)$\sf{Sec^{2} O = 1 + tan^{2} O}$

Answer 2

Step-by-step explanation:

Given:

${ \cosec}^{2} 57 - { \tan}^{2} 33$

To find: Value of trigonometric expression is

a) 0

b) 1

c) -1

d) 2

Solution:

Tip: Identities used

$1)\bf { cosec}(90 - \theta) = sec \: \theta$

$2)\bf 1 + {tan}^{2}\theta = {sec}^{2} \theta$

Step 1: Convert $\cosec \: \theta$ into $\sec \: \theta$ by applying first identity.

${ \cosec}^{2} (90 - 33) - { \tan}^{2} 33$

$= { \sec}^{2} (33) - { \tan}^{2} 33$

Step 2: Use identity 2

From identity 2 it is clear that

${ \sec}^{2} 33- { \tan}^{2} 33 = 1$

Option b is correct.

Final answer:

$\bf { cosec}^{2} 57 - { tan}^{2} 33 = 1$

Option b is correct.

Hope it helps you.

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