Prove that, $\frac{\left(1+{\tan }^2\theta \right)\cot \theta }{{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}}^2\theta }=\tan \theta$.

Important Questions on Trigonometric Identities

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 63

Prove that, ${\left(\mathrm{t}\mathrm{a}\mathrm{n}\theta +\frac{1}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }\right)}^2+{\left(\mathrm{t}\mathrm{a}\mathrm{n}\theta -\frac{1}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }\right)}^2=2\left(\frac{1+{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }{1-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }\right)$.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 64

Prove that, $\left(\frac{1}{{\mathrm{s}\mathrm{e}\mathrm{c}}^2\theta -{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }+\frac{1}{{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}}^2\theta -{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }\right){\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta {\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta =\frac{1-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta {\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }{2+{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta {\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }$.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 65

Prove the following identities:  ${\left(\frac{1+\mathrm{s}\mathrm{i}\mathrm{n}\theta -\mathrm{c}\mathrm{o}\mathrm{s}\theta }{1+\mathrm{s}\mathrm{i}\mathrm{n}\theta +\mathrm{c}\mathrm{o}\mathrm{s}\theta }\right)}^2=\frac{1-\mathrm{c}\mathrm{o}\mathrm{s}\theta }{1+\mathrm{c}\mathrm{o}\mathrm{s}\theta }$.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 65

Prove that,  $\frac{1+\mathrm{s}\mathrm{e}\mathrm{c}\theta -\mathrm{t}\mathrm{a}\mathrm{n}\theta }{1+\mathrm{s}\mathrm{e}\mathrm{c}\theta +\mathrm{t}\mathrm{a}\mathrm{n}\theta }=\frac{1-\mathrm{s}\mathrm{i}\mathrm{n}\theta }{\mathrm{c}\mathrm{o}\mathrm{s}\theta }$.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 66

Prove that, $(\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{A}+\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{A}-1)(\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{A}-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{A}+1)=2\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{A}$.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 67

Prove that, $(1+\cot A-cosec A)(1+\tan A+\sec A)=2$.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 68

Prove that, $(cosec \theta -\sec \theta )(\cot \theta -\tan \theta )=(cosec \theta +\sec \theta )(\sec \theta cosec \theta -2)$.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 11 - Trigonometric Identities>EXERCISE 11.1>Q 69

Prove that, $(\sec A-cosecA)(1+\tan A+\cot A)=\tan A \sec A-\cot A\mathit{ }cosec A$.