Question

tan 20*tan 70+cosec 40*cos50+sin^245

Answer 1

Step-by-step explanation:

SOLUTION IS IN THE ATTACHMENT

Trigonometry is the study of the relationship between the sides and angles of a triangle.

Two angles are said to be complementary of their sum is equal to 90° .

θ & (90° - θ) are complementary angles.

An equation involving trigonometry ratios of an angle is called is called a trigonometric identity, if it is true for all values of the angles involved. For any acute angle θ, we have 3 identities.

i) sin² θ + cos² θ = 1 ,ii) 1 + tan² θ = sec² θ , iii) cot² θ +1 = cosec² θ.

Hence, the value of (cos²20°+cos²70°/ sec²50°– cot²40°) + 2 Cosec² 58° – 2 Cot 58° tan 32°–4 tan 13° tan 37° tan77° tan 45° tan 53° is -1.

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Answer 2

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Trigonometry is the study of the relationship between the sides and angles of a triangle.

Two angles are said to be complementary of their sum is equal to 90° .

θ & (90° - θ) are complementary angles.

An equation involving trigonometry ratios of an angle is called is called a trigonometric identity, if it is true for all values of the angles involved. For any acute angle θ, we have 3 identities.

i) sin² θ + cos² θ = 1 ,ii) 1 + tan² θ = sec² θ , iii) cot² θ +1 = cosec² θ.

Hence, the value of (cos²20°+cos²70°/ sec²50°– cot²40°) + 2 Cosec² 58° – 2 Cot 58° tan 32°–4 tan 13° tan 37° tan77° tan 45° tan 53° is -1.