Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
ChatGPT
Sign up
Use trigonometric identities to transform the left side of the equation into the right side (0 < theta < /2).
sinθ/cosθ + cosθ/sinθ = cscθsecθ
Full explanation
ChatGPT
To transform the left side of the equation
sin
cos
+
cos
sin
cosθ
sinθ
+
sinθ
cosθ
into
csc
sec
cscθsecθ, we'll use trigonometric identities step by step.
Start with the given expression:
sin
cos
+
cos
sin
cosθ
sinθ
+
sinθ
cosθ
Find a common denominator:
To combine these fractions, we need a common denominator. The common denominator here is
sin
cos
sinθcosθ.
sin
2
sin
cos
+
cos
2
sin
cos
sinθcosθ
sin
2
θ
+
sinθcosθ
cos
2
θ
Combine the fractions:
sin
2
+
cos
2
sin
cos
sinθcosθ
sin
2
θ+cos
2
θ
Apply the Pythagorean identity:
Recall that
sin
2
+
cos
2
=
1
sin
2
θ+cos
2
θ=1. Substitute this identity into the expression:
1
sin
cos
sinθcosθ
1
Express in terms of cosecant and secant:
Now, rewrite
1
sin
cos
sinθcosθ
1
using the identities:
1
sin
cos
=
csc
sec
sinθcosθ
1
=cscθsecθ
Therefore, we have shown that:
sin
cos
+
cos
sin
=
csc
sec
cosθ
sinθ
+
sinθ
cosθ
=cscθsecθ
This completes the transformation using trigonometric identities.:
Step-by-step explanation:
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
