# Challenging O Level Trigonometry Question (A Maths)

A reader of our Mathtuition88.com blog asked the following Maths question:

Given that $\sin x+\sin y=a$ and $\cos x+\cos y=a$, where $a\neq 0$, express $\sin x+\cos x$ in terms of $a$.

This is a rather challenging question, since there are many options to start. Which formula(s) should we use? Factor formula? R-formula? Give it a try first if you want to have a challenge.

Solution:

It turns out we can write: $\sin y=a-\sin x$

#### $\cos y=a-\cos x$

Then, use $\sin^2 y+\cos ^2 y=1$ $(a-\sin x)^2+(a-\cos x)^2=1$

Expanding, $a^2-2a\sin x+\sin^2 x+a^2-2a\cos x+\cos^2 x=1$

Rearranging, $2a^2-2a(\sin x+\cos x)+1=1$ $2a(a-(\sin x+\cos x))=0$

Since $a\neq 0$, we have $a-(\sin x+\cos x)=0$.

Thus, $\boxed{\sin x+\cos x=a}$.

Featured book:  Schaum’s Outline of Trigonometry, 5th Edition: 618 Solved Problems + 20 Videos (Schaum’s Outline Series) #### Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately, there’s Schaum’s. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems–it’s just like having your own virtual tutor! You’ll find everything you need to build confidence, skills, and knowledge for the highest score possible.

More than 40 million students have trusted Schaum’s to help them succeed in the classroom and on exams. Schaum’s is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum’s Outline gives you

• 618 fully solved problems to reinforce knowledge
• Concise explanations of all trigonometry concepts
• Updates that reflect the latest course scope and sequences, with coverage of periodic functions and curve graphing.

Fully compatible with your classroom text, Schaum’s highlights all the important facts you need to know. Use Schaum’s to shorten your study time–and get your best test scores!

Schaum’s Outlines–Problem Solved. ## Author: mathtuition88

https://mathtuition88.com/

## One thought on “Challenging O Level Trigonometry Question (A Maths)”

This site uses Akismet to reduce spam. Learn how your comment data is processed.