Question

If y sin 45° cos 45° = tan2 45° – cos2 30°, then y =___________ (a) -1/2 (b) 1/2 (c) -2 (d) 2

Answer 1

Answer:

b. 1/2

Step-by-step explanation:

I have attached photo of the Solution. trick is to remember the values of sins , cos and tans of basic angles. hop it was helpful!

Answer 2

The correct option is (b) 1/2

Given : y sin 45° cos 45° = tan² 45° – cos² 30°

To find : To choose the correct option

y = ______

(a) - 1/2

(b) 1/2

(c) - 2

(d) 2

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

y sin 45° cos 45° = tan² 45° – cos² 30°

Step 2 of 2 :

Find the value of y

y sin 45° cos 45° = tan² 45° – cos² 30°

$\displaystyle \sf{ \implies y \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } = {1}^{2} - { \bigg( \frac{ \sqrt{3} }{2} \bigg)}^{2} }$

$\displaystyle \sf{ \implies \frac{y}{ 2} = 1 - \frac{3}{4} }$

$\displaystyle \sf{ \implies \frac{y}{ 2} = \frac{4 - 3}{4} }$

$\displaystyle \sf{ \implies \frac{y}{ 2} = \frac{1}{4} }$

$\displaystyle \sf{ \implies y= \frac{2}{4} }$

$\displaystyle \sf{ \implies y= \frac{1}{2} }$

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