Question

Without using the trigonometric tables, find the values of :
iv) cos 90° + :cos^2 45° sin 30° tan 45°​

Answer 1

Step-by-step explanation:

The Trigonometric Table will be required to solve this question. Refer that in your book.

I have written the direct Values :-

$\sf{cos \ 90 = 0}$

$\sf{cos \ 45 = \dfrac{1}{\sqrt{2}}}$

$\sf{sin \ 30 = \dfrac{1}{2}}$

$\sf{tan \ 45 = 1}$

Now, placing the values, we can easily solve this question.

cos 90° + cos² 45° sin 30° tan 45°

cos² 45° will be 1/2.

$\sf{0 + \dfrac{1}{2} \times \dfrac{1}{2} \times 1}$

So, the answer which we get after simplifying the expression is 1/4.

☆Refer to the Trigonometric Table for all purpose of attempting the question or you might get muddled.

Answer 2

Answer:

We know that

$\sf cos \; 90^\circ = 0$

$\sf cos^2 \; 45^\circ = \bigg(\dfrac{1}{\sqrt{2}}\bigg)^2$

$\sf sin \; 30^\circ = \dfrac{1}{2}$

$\sf tan \; 45^\circ = 1$

By putting value

$\sf 0 + \bigg(\dfrac{1}{\sqrt{2}}\bigg)^2 \times \dfrac{1}{2} \times 1$

$\sf 0 + \dfrac{1}{2} \times \dfrac{1}{2} \times 1$

$\sf 0 + \dfrac{1}{4} \times 1$

$\sf 0 + \dfrac{1}{4}$

1/4