Question

if sin theta =5 by 13 and theta is an acute angle, find the value of tan theta +1 by cos theta
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Answer 1

Answer:

1.5

Step-by-step explanation:

sin theta =5 / 13 =0.3846

tan theta +1 / cos theta

(sin theta/cos theta) + (1 / cos theta)

(sin theta + 1)/cos theta

(0.3846 + 1)/cos theta

1.3846/cos theta = x

squaring,

(1.3846)^2/cos^2 theta = x^2

1.9171/1-sin^2 theta = x^2

1.9171/1-(0.3752)^2 = x^2

1.9171/0.8592 = x^2

2.231 = x^2

x =1.4937 ~ 1.5

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Answer 2

Step-by-step explanation:

Given If sin theta = 5 / 13 and theta is an acute angle, find the value of tan theta + 1 / cos theta

• So sin theta = 5/13
• We need to find the value of tan theta + 1 / cos theta
• So we have the identity
•                    sin^2 theta + cos^2 theta = 1
•                        (5/13)^2 + cos^2 theta = 1
•                                     cos^2 theta = 1 – (5/13)^2
•                                     cos^2 theta = 1 – 25 / 169
•                                     cos^2 theta = 144 / 169
•                                     Or cos theta = 12/13
•        Now we have
•                                   tan theta + 1/cos theta
•                                      sin theta + 1 / cos theta
•                                           5/13 + 1/12/13
•                                                    18 / 13 x 13 / 12
•                                                         = 18 / 12
•                                                         = 3/2
• Also it can be done by using pythagoras theorem

Reference link will be

https://brainly.in/question/14745776