Problem 7 Easy Difficulty

Express $\sin 67^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.

Answer

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Precalculus

NCERT Class 10 - Math

Chapter 8

Introduction to Trigonometry

Section 3

Trigonometric Ratios of Some Specific Angles

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Video Transcript

So in the given question we are told to express the Terms sign of 67°.. Bless Cost of 75° in terms of Angers in between zero and 45 degrees. Right? So what we can do over here is we can use the relation that sign theater can also be written as cost of 90 minus think to and const data can be written as a sign of 90 minus theta. So then what we can do here is that we can take sine of the angle 67 And we can write it as a cost of 90 -67 Night and 90 -67 is equal to 23. So we have a sign of 67 can be written us Cost of 23° And then we have a cost of 75 which we can write a sign of 90 -75 which is an equal to sign off 90 -75 years 15. So we wrote both signed 67 and cost 75 us it as techno metric ratios, that of the angles in between zero and 45 degrees. And now the expression can be written. Us costs 23 degrees plus sign 15 degrees. Insular. Signed 67 plus, cost 75. So I hope you understood the method. Thank you.

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